Detecting diagnostic events in a thermal system

ABSTRACT

Embodiments of the disclosure provide a thermal model based on an adaptive filter bank for characterizing heat transfer of a volume of a thermal system. In one embodiment, the adaptive filter bank is used for diagnostics that provides information related to the condition of a thermal system. The diagnostics are based on an analysis of heat transfer characteristics of a dynamic representation of the thermal system. In accordance with the embodiments, thermal coefficients are generated based on an adaptive filter bank. One or more filters are applied to the thermal coefficients based on a sampling rate and one or more estimate thermal coefficient thresholds are generated based on the sampling rate. It is determined whether at least one of the thermal coefficients that is filtered satisfies at least one of the estimated thermal coefficient thresholds. Thereupon, alert information indicative of a diagnostic event is provided based on the determination.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 16/519,751, filed Jul. 23, 2019, which is hereby incorporatedby this reference in its entirety.

TECHNICAL FIELD

The disclosure relates to generally to thermal models, and moreparticularly, to detecting diagnostic events in a thermal system.

BACKGROUND

Users often use devices to control or modify the temperatures in certainsites, such as a residence. Such devices, however, may be unable tolearn or express the heat transfer characteristics of a thermal system.Thermal models exploit observed physical relationships related to deviceproperties and weather estimates to characterize heat transfer andpredict temperature and power consumption, facilitating optimaltemperature control, with improved thermal comfort and reduced powerconsumption.

BRIEF DESCRIPTION OF THE DRAWINGS

A more detailed description of the disclosure, briefly summarized above,can be had by reference to various embodiments, some of which areillustrated in the appended drawings. While the appended drawingsillustrate select embodiments of this disclosure, these drawings are notto be considered limiting of its scope, for the disclosure can admit toother equally effective embodiments.

FIG. 1 is a block diagram illustrating a system architecture associatedwith a thermal system according to an embodiment of the disclosure.

FIG. 2 is an example of an adaptive filter according to an embodiment ofthe disclosure.

FIG. 3 is another example of an adaptive filter bank according to anembodiment of the disclosure.

FIG. 4 is an example graph illustrating a thermal model adaptive filtersolution according to an embodiment of the disclosure.

FIG. 5 is a flow diagram of a method of implementing an adaptive filterbank for modeling a thermal system according to an embodiment of thedisclosure.

FIG. 6 is a flow diagram of another method of implementing an adaptivefilter bank for modeling a thermal system according to an embodiment ofthe disclosure.

FIG. 7 is a flow diagram of a method of detecting diagnostic events in athermal system in view of an adaptive filter bank according to anembodiment of the disclosure.

FIGS. 8A-8D are example graphs illustrating diagnostic event dataaccording to an embodiment of the disclosure.

FIG. 9 is a block diagram illustrating a machine in which embodiments ofthe disclosure can be used.

Identical reference numerals have been used, where possible, todesignate identical elements that are common to the figures. However,elements disclosed in one embodiment can be beneficially utilized onother embodiments without specific recitation.

SUMMARY

In accordance with the disclosure, a thermal model solution is provided.The thermal model solution implements an adaptive filter bank tocharacterize heat transfer associated with one or more volumes of athermal system. In implementations, the thermal models interact with oneor more thermal devices in a zone and a weather model associated with asite, to construct, adapt, and verify, a set of thermal coefficientswhich characterize heat transfer and exploit the observed relationshipbetween environmental conditions, including temperature, and powerconsumption. The thermal model requires no commissioning information tocharacterize heat transfer, but rather extracts information entirelyfrom passive observation of data provided by the thermal devices and theweather model. For example, the thermal model uses the passiveobservations to determine the heat transfer data associated with sitebased on the relationships between environmental conditions,temperatures, power consumption and other type of physicalcharacteristics associated with the zones. In some situations, certaininformation regarding the zones may be unknown or unreliably reported,such as the specific geometry of each zone and the thermal mass and heattransfer characteristics of boundary materials. This unknown orunreliable information can lead to errors in characterization of heattransfer, which can result in an inefficient or wasteful use of energyby the system for comfort-based management of site that is associatedwith the system architecture.

Implementations of the disclosure address the above-mentioned and otherdeficiencies by implementing an adaptive filter bank to minimize theestimation error that can occur when characterizing the heat transferassociated with one or more volumes of a thermal system. One exampleapplication of the adaptive filter bank may be used for diagnostics thatprovides information related to the condition of a thermal system. Thediagnostics may be based on an analysis of heat transfer characteristicsof a dynamic representation of the thermal system. In that regard, thediagnostic events may indicate detection of a change in observed orestimated characteristics of the thermal system which may be related todefective or anomalous operation.

In one embodiment, a method is provided. The method includes generating,by a controller device, thermal coefficients at an adaptive filter bankto characterizes heat transfer of a volume associated with a thermalsystem; applying, by the controller device, one or more filters to thethermal coefficients based on a sampling rate; responsive to theapplying the filters, generating, by the controller device, one or moreestimate thermal coefficient thresholds based on the sampling rate;determining, by the controller device, whether at least one of thethermal coefficients that is filtered satisfies at least one of theestimated thermal coefficient thresholds; and providing, by thecontroller device, alert information indicative of a diagnostic eventassociated with the thermal system based on the determining.

In another embodiment, a system is provided. The system includes amemory to store a plurality of thermal coefficient data; and acontroller device, operatively coupled to the memory, to: generatethermal coefficients at an adaptive filter bank to characterizes heattransfer of a volume associated with a thermal system; apply or morefilters to the thermal coefficients based on a sampling rate; responsiveto applying the filters, generate one or more estimate thermalcoefficient thresholds based on the sampling rate; determine whether atleast one of the thermal coefficients that is filtered satisfies atleast one of the estimated thermal coefficient thresholds; and providealert information indicative of a diagnostic event associated with thethermal system based on the determining.

In yet another embodiment, a non-transitory computer-readable storagemedium is provided. The non-transitory computer-readable storage mediumincludes executable instructions that when executed, by a controllerdevice, cause the controller device to: apply, by the controller device,or more filters to the thermal coefficients based on a sampling rate;responsive to applying the filters, generate one or more estimatethermal coefficient thresholds based on the sampling rate; determinewhether at least one of the thermal coefficients that is filteredsatisfies at least one of the estimated thermal coefficient thresholds;and provide alert information indicative of a diagnostic eventassociated with the thermal system based on the determining.

In one example, generating the thermal coefficients further includesidentifying a thermal model for application with the thermal system;determining, based on the thermal model, an estimation error for areference signal with respect to a primary signal associated with thevolume; and adapting, based on the adaptive filter, the thermalcoefficients in view of the estimation error to satisfy a solutionassociated with the volume. In another example, the sampling rate isadapted based on a filter operation associated with at least one of thefilters, where the filter operation includes at least one infiniteimpulse response filter. In yet another example, generating the estimatethermal coefficient thresholds further includes: determining whether asequence of thermal coefficient vectors support a definition of thediagnostic event. Further, it is determined whether the at least onethermal coefficient exceeds an upper or lower boundary window associatedwith the at least one estimated thermal coefficient threshold. In thatregard, the alert information indicates an anomalous operation of adevice associated with the volume.

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used as an aid in determining the scope of the claimed subjectmatter. Other features will be in part apparent and in part pointed outhereinafter.

DETAILED DESCRIPTION

Aspects of the disclosure generally relates to implementing a thermalmodel based on an adaptive filter bank to characterize the heat transferof a volume of a thermal system. The techniques of the disclosure mayuse the adaptive filter bank to improve the performance characteristics,diagnostics, energy saving estimations and optimal temperature control(including optimal start and optimal stop) of applications forcontrolling desired temperatures in one or more volumes of the thermalsystem. In accordance with the disclosure, the adaptive filter bankhelps minimize estimation error that can occur when characterizing theheat transfer. In one embodiment, the adaptive filter bank may consumean incident signal that characterizes heat transfer propertiesassociated with a volume of the thermal system, produce a referencesignal which estimates an observed primary signal, calculate anestimation error, and adapt thermal coefficients to minimize estimationerror.

An incident signal includes observed data and weather estimates relatedto active, passive, solar irradiance and unobserved heat transfer in oneor more volumes of the thermal system. A thermal coefficient vector is arepresentation of the heat transfer characteristics associated with aspecific volume of a thermal system, including passive, active, solarirradiance, and unobserved heat transfer. A thermal coefficient vectormay be initialized to represent typical or expected heat transfercharacteristics of a volume and adapted to improve reference signalestimation. A reference signal represents an estimated rate oftemperature change associated with a volume of a thermal system and isgenerated from a difference equation based on an incident signal, athermal coefficient vector, and the state of an adaptive filter bank. Aprimary signal represents an observed rate of temperature change in avolume of a thermal system, which may be calculated from temperaturesreceived from a thermal control unit that is monitoring temperatures andother relevant data associated with a volume.

An estimation error is calculated based on the difference between theprimary signal and the reference signal and represents an estimationerror associated with using a reference signal from an adaptive filterbank at a specific state to estimate a primary signal. A thermalcoefficient vector is adapted based on estimation error, in order tominimize subsequent estimation error according to a specified metric.Over a sequence of adaptations, thermal model coefficients converge torepresent the heat transfer characteristics of a volume of a thermalsystem. Adaptation may be continuous, as convergence may be stationary,quasi-stationary, or dynamic, according to the operating condition ofthe thermal system, and estimation error is generally improved withincreased diversity in incident signal observations.

An example application of the adaptive filter bank may be used fordiagnostics that provides information related to the condition of athermal system. The diagnostics may be based on an analysis of heattransfer characteristics of a dynamic representation of the thermalsystem. In that regard, the diagnostic events may indicate detection ofa change in observed or estimated characteristics of the thermal systemwhich may be related to defective or anomalous operation. In someembodiments, the diagnostic events may be generated due to evaluation ofobservations and estimates, over various time intervals which supportclassification as, for example, transient or persistent. For example, atransient diagnostic event detection may include pump, valve, or relayfailures, in hydronic heating systems, or relay failure or rapidrefrigerant leaks in air-based furnace, heat pump, or air conditioningsystems. In other examples, a persistent diagnostic event detectionincludes slow boiler, pipe, or radiator water leaks, or sludgeaccumulation due to oxidization, in hydronic systems, or slowrefrigerant leaks, damaged heat exchangers, or contaminated ducts andfilters in air-based systems. In some examples, the transient diagnosticevent may demonstrate either cyclic or quasi-periodic or persistentbehavior, which may be caused by conditions including a slow water leakin a hydronic system, as an occupant may either be aware of the defectand elect to occasionally replace water and restore normal operations orallow the defect to evolve into persistent and increasingly anomalousoperation.

To implement the diagnostics for a thermal system, a thermal model isconstructed, initialized, and adapted (e.g., using the adaptive filterbank) on a per zone basis to produce a dynamic estimate of thermalcoefficient data. This thermal coefficient data is used to describe andestimate the behavior of that thermal system. Then, a filter is appliedto the thermal coefficient data based on a sampling rate. For example, asampling rate may be adapted and electively combined with filteroperations to reduce aliasing and implement rate adaptation, therebyconverting the thermal coefficient data to an effective sample period.In response to applying the filter, one or more estimate thermalcoefficient thresholds are generated. Thereupon, it is determined that adiagnostic event associated with the thermal system is detected based onwhether the thermal coefficient data satisfies a corresponding estimatedthermal coefficient threshold. In such case, an alert or warning messageis generated indicated that some component of the thermal system may bemalfunctioning or experiencing an anomalous operation due to abnormalconditions.

System Architecture

FIG. 1 is a block diagram illustrating a system architecture 100associated with a thermal system according to an embodiment of thedisclosure. A thermal system (also referred to as a site 101) may bedescribed as a collection of interdependent volumes whose thermalbehavior is described by the transfer of mass, work, and heat across thevolume boundaries. Each volume is defined as a zone 103 that includes acontiguous region of uniform thermal control. In some embodiments, thesystem architecture 100 may implement a system for comfort-basedmanagement of the thermal system, including residential and commercialbuildings with active cooling and/or heating is described, with anemphasis on practical applications.

In some embodiments, the comfort-based management associated with systemarchitecture 100 adaptively and continuously learns the heat transfercharacteristics of a thermal system, and the thermal comfortcharacteristics of the occupants, to facilitate optimal temperaturecontrol which minimizes power consumption while maintaining thermalcomfort. Although embodiments of the disclosure are described inaccordance with a certain type of system, this should not be consideredas limiting the scope or usefulness of the features of the disclosure.For example, the features and techniques described herein can be usedwith other types systems, system architectures, local embeddedcontrollers and/or distributed cloud computing environment.

As shown in FIG. 1, an illustrative example of the system architecture100 is implemented in a distributed cloud-computing environment 105. Thedistributed cloud-computing environment 105 supports scalabledistributed computing and storage in which one or more remote computingnodes 107 and relatively simple distributed devices that may include,for example, one or more thermal control units 102 which interact withone or more Heating Ventilation Air Conditioning (HVAC) units 104. Theone or more remote computing nodes 107 may execute software and/or otherprocesses. Each computing node 107 may refer to a virtual server, forexample, of a physical machine, a memory partition, or any other type ofcomputing environment and provide a full or partially isolated executionenvironment for the execution of an application.

Cloud computing environment 105 may achieve scalability through flexibleresource allocation, often virtualizing servers 130 and computing nodes107 which are abstracted from the physical hardware on which theyreside. For example, resources can be dynamically allocated and disposedon demand, abstracting infrastructure complexity from computing nodes107. In some embodiments, the computing nodes 107 are virtual machinesthat are hosted on a physical machine. The computing nodes 107 interactwith distributed devices, such as thermal control unit 102 and HVACunits 104, via a network 106, to facilitate data transport, archival,and synchronization, and manage computational and storage resources,dynamically allocating and disposing of other services and jobs tosupport system architecture 100. In some embodiments, the network 106may be a private network (e.g., a local area network (LAN), Wi-Fi,Bluetooth, Radio Frequency), a wide area network (WAN), intranet, etc.),or a public network (e.g., the Internet), etc.

Server 109 manages computational and storage resource allocation anddisposal, facilitates data transport and synchronization, and interactswith one or more weather services 110, one or more sites 101, and one ormore computing nodes 107. Computing node 107 is a collection of entitieswhich implement the analysis and control capabilities and interacts withserver 100 to execute comfort based thermal management of the one ormore sites 101. A site 101 contains one or more zones 103. Each zone 103contains one or more thermal control units 102, which interact with aserver 109 and one or more HVAC units 104. For each supported site 101,a computing node 107 includes a comfort agent 120, a comfort model 130for each zone 103, a thermal model 140 for each zone 103, one or morethermal devices 150 for each zone 103, a weather model 160.

Weather Model

Weather model 160 interacts with server 100 to exchange information withweather service 110. In some embodiments, the weather model 140 is arepresentation of the weather service 110 that defines forecastestimations of properties of weather conditions. These weatherconditions may be relevant in a specific region of interest thatincludes the surrounding environment of site 101. For example, a weatherestimation provided by the weather service 110 can indicate a cloudcover, humidity, solar irradiance, and/or temperature of one or moreareas. The weather model 160 may estimate future conditions indirectlyfrom the weather service 110, which provides properties at a defaultresolution (e.g., nominally one (1) hour) over a weather duration (e.g.,nominally twenty-four (24) hours), and a finite geographical range ofsupport that includes a site 101, location, city, region and/or thelike. In some embodiments, the weather model 160 can have a uniqueassociation with a specific region of interest and the weather service110 properties can require spatial or temporal interpolation to achievea specified effective resolution or improve accuracy.

Thermal Device

Thermal device 150 interacts with server 109 to exchange informationwith a thermal control unit 102 in a zone 103. In some embodiments, athermal device 150 may be represented as a specific thermal control unitwhich observes and controls the temperature of a volume (e.g., zone 103)of a thermal system (e.g., site 101). For example, the thermal controlunit 102 can support active cooling and/or heating associated with thevolume. For example, active cooling employs a cooling type HVAC unit104, e.g., including an air conditioner, refrigerator, or freezer, tocool a zone 103, while active heating employs a heating type HVAC unit104, e.g., including a furnace, heat pump, resistive heating, orelectric or hydronic radiant heating, to heat a zone 103. An HVAC unit104 can comprise any device capable of controlling temperature, byproducing, consuming, or transferring heat, in a zone 103. In thisregard, active cooling and heating are mutually exclusive at a specifictime. In some embodiments, the thermal control unit 102 can supportoccupant interactions, which indicate a preference to lower or raise thetemperature associated with the zones 103 of site 101. The thermaldevice 150 can provide an immediate and transient response to increasethe thermal comfort of an occupant in response to occupant interactions,by lowering or raising the temperature by a temperature offset over afinite duration.

Comfort Agent

Comfort agent 120 interacts with server 100, and observes one or morecomfort models 130, and one or more thermal models 140 associated with asite 101. The comfort agent 120 interacts with comfort models 130 toestablish constraints on temperature controls, and with thermal models140 to define a collection of physically realizable states andassociated energy or power transitions. This allows the comfort agent120 to facilitate optimal temperature control in each zone 103 in ofsite 101, which minimizes power consumption while maintaining thermalcomfort. The optimal temperature controls facilitate an optimal startand optimal stop settings for the thermal devices 150, which dynamicallyadvance control temperature transitions associated with active coolingor heating to compensate for heat transfer latency. This ensures thatthe advance control temperature transitions continue to respect definedconstraints, which are physically realizable relative to anticipatedenvironmental conditions, and opportunistically reduce powerconsumption.

The comfort agent 120 interacts with the comfort models 130 to establishtemperature constraints which bound temperature control, and withthermal models 140 to define a collection of physically realizablestates and associated energy or power transitions, to facilitate optimaltemperature control in each zone 103 in site 101, which minimizes powerconsumption while maintaining thermal comfort. In some embodiments, thecomfort agent 120 defines a cost function in terms of energy, power,currency, resource availability, or time, associated with optimal paths125 formed by constrained state transitions over a control duration. Thecomfort agent 120 uses the thermal models 140 in conjunction with thecomfort models 130 to select the optimal path with represents a seriesof state transitions that minimize cost in the context of anticipatedutility and environmental conditions. Specific methods employed by thecomfort agent 120 to select an optimal path may be consistent with anapplication of reinforcement machine learning.

An optimal path 125 is selected by the comfort agent 120, as asequential collection of states, with an epoch of a root state aterminus of a state at a terminus of a control duration, N, where anaction value vector, q _(u,v,c,n), from state index u to state index v,in cool state c, at sample n, is selected to correspond to a specifictransition selected to assign a state value vector, s _(u,c,n), inestimation. As such, the optimal path 125 is the sequence of stateswhich when traversed minimizes a root state value vector, s _(u,c,n). Insome embodiments, the optimal path includes optimal start and optimalstop settings for the thermal devices 150. Optimal start advances acontrol temperature transition to a higher energy state to ensure that adevice temperature, T_(i,n), in zone 103 i, at sample n, observed at aspecified control temperature transition is within a control offset,T_(C), of an effective temperature, T_(E,i,j,c,n), in cool state c.Optimal stop advances a control temperature transition to a lower energystate to ensure that a device temperature, Ti,n, in zone 103 i, atsample n, observed at a specified control temperature transition iswithin a control offset, T_(C), of an effective temperature,T_(E,i,j,c,n), in cool state c. Optimal start and optimal stop areintegral behaviors expressed in an optimal path 125 extracted from acollection of states which defines more than one path. However, optimalstart and optimal stop behaviors are elective and separable in a simplesequential solution.

Comfort Model

Comfort model 130 is a representation of the thermal comfort in a zone103. The comfort model 400 can estimate an effective temperature atwhich an occupant is unlikely to object, for example thereby maintainingoccupant comfort, while minimizing energy consumption due to activecooling and/or heating. An effective temperature represents thetemperature associated with the lowest thermal device power consumptionat which the occupants are unlikely to object. An estimation ofeffective temperature facilitates applications including optimaltemperature control, demand response, and virtual power plantcapabilities. Thermal comfort, in many aspects, may be a subjectiveproperty that may not be agreed upon by the occupants in zone 103, andthe estimation of effective temperatures at which all occupants wouldconsistently express similar satisfaction is perhaps not an entirelyreasonable expectation.

The comfort model 130 addresses the issue of defining thermal comfort byconstructing and adapting a collection of temperature profiles 137. Thetemperature profiles 137 are used to learn patterns of behavior byinteractions with occupants, and by adapting temperature profiles 137 toopportunistically minimize power consumption due to active cooling oractive heating at the site 103 while also characterizing thermalcomfort. The comfort model 130 requires no commissioning information,does not utilize occupancy estimation, and extracts information requiredto characterize thermal comfort entirely from passive observation ofdata and events provided by associated thermal devices 150. For example,the comfort model 130 can learn multiple independent temperatureprofiles 137 through observation of the temperature (e.g., of a zone103), and through occupant interactions, which indicate a preference tolower or raise the temperature. A control state is associated with acomfort model 130, to allow or prevent modification of associatedtemperature profiles137, to allow the comfort based thermal managementsystem to continue to observe and learn from temperature and powerconsumption patterns, even when the occupants have elected to disableoptimal temperature control. If a control state associated with acomfort model 130 prevents modification of associated temperatureprofiles 137 related to learned behavior, alternative temperatureprofiles which reflect a schedule of temperature transitions specifiedby the occupants are employed. An independent temperature profiles 137associated with each day of the week may be defined by the occupants andretained, without modification, until it is electively replaced. Statictemperature profiles 137 also form a suitable basis for application ofoptimal start and optimal stop behaviors.

Thermal Model

Thermal model 140 is a representation of the thermal behavior of avolume in a thermal system, which characterizes heat transfer data 145,and estimates energy consumption and temperature in a thermal system.For example, the thermal system may be represented by site 101 and canbe generalized as a collection of interdependent volumes defined as zone103 with boundaries and a surrounding environment, whose behavior isdescribed by the transfer of mass, work, and heat across the boundaries.In some embodiments, the thermal systems supported by the thermal model140 as described may reasonably apply assumptions of open mechanicallyisolated operation and simple transient conduction when determining theheat transfer data 142. It should be noted that open mechanicallyisolated thermal systems do not support deformation in volumes, andassociated work transfer, or mass transfer across a boundary. A thermalsystem, such as site 101, may be conveniently described as open andmechanically isolated, if it does not support deformation, and/or if themass within a volume is quasi-stationary, or changes slowly relative tothe rate of heat transfer. In such as case, the thermal model 140 canemploy simple transient conduction to simplify analysis by neglectingtemperature and pressure gradients within a volume (e.g., zone 103) byassuming that heat is conducted within the volume much faster than heattransfer across a boundary.

Heat Transfer

With respect to the heat transfer data 142 characterized by the thermalmodel 140, heat transfer,

${\frac{d}{dt}\left( Q_{i,c,t} \right)},$

to zone 103 i, at time t, is a measure of the aggregate rate of thermalenergy change from various sources, including passive heat transfer,

${\frac{d}{dt}\left( Q_{{Pi},t} \right)},$

active heat transfer,

${\frac{d}{dt}\left( Q_{{Ai},{c.t}} \right)},$

solar heat transfer,

${\frac{d}{dt}\left( Q_{{Si},t} \right)},$

and unobserved heat transfer,

${\frac{d}{dt}\left( Q_{{Ui},t} \right)},$

which is represented by the following equation:

${\frac{d}{dt}\left( Q_{i,c,t} \right)} = {{\frac{d}{dt}\left( Q_{{Pi},t} \right)} + {\frac{d}{dt}\left( Q_{{Ai},c,t} \right)} + {\frac{d}{dt}\left( Q_{{Si},t} \right)} + {\frac{d}{dt}\left( Q_{{Ui},t} \right)}}$

Passive heat transfer,

${\frac{d}{dt}\left( Q_{{Pi},t} \right)},$

to zone 103 i, at time t, is equal to the product of thermaltransmittance, h_(Pi,j), a property related to the heat transfercharacteristics of the boundary material, the surface area of the sharedzone boundary, A_(Pi,j), and the difference between the temperature inzone j, T_(j,t), and the temperature in zone j, T_(i,t), in a site withJ-1 zones, which is represented by the following equation:

${\frac{d}{dt}\left( Q_{{Pi},t} \right)} = {{\sum\limits_{\underset{j \neq i}{j = 0}}^{J}{\frac{d}{dt}\left( Q_{{Pi},j,t} \right)}} = {\sum\limits_{\underset{j \neq i}{j = 0}}^{J}{h_{{Pi},j}{A_{{Pi},j}\left( {T_{j,t} - T_{i,t}} \right)}}}}$

With reference to the above, the passive heat transfer relative to thesurrounding environment follows Newton's Law of Cooling in a mannersimilar to inter-zone passive heat transfer, and thus may be modeled asa separate zone, for notational convenience. In embodiments, the passiveheat transfer, to a zone 103 i across a boundary from an adjacent zonej, is extended by superposition to aggregate the passive heat transferfrom each zone j which may share a boundary with zone 103 i, though therelative geometry and connectivity of the zones with a site is unknown.Inter-zone passive heat transfer may be electively neglected betweenzone j and zone i, if the temperatures in the zones are observed to besufficiently similar, as the resulting temperature differences may berelatively insignificant and insufficiently diverse, resulting in asolution which is ill-conditioned.

Active heat transfer,

${\frac{d}{dt}\left( Q_{{Ai},c,t} \right)},$

to zone 103 i, in cool state c, at time t, is equal to the aggregateproduct of thermal efficiency,

_(i,c,k), defined as the ratio of power produced or transported, andpower, P_(i,c,k,t), consumed in unit index k, of K units, which isrepresented by the following equation:

${\frac{d}{dt}\left( Q_{{Ai},c,t} \right)} = {{\sum\limits_{k = 0}^{K - 1}{\frac{d}{dt}\left( Q_{{Ai},c,k,t} \right)}} = {\sum\limits_{k = 0}^{K - 1}{\eta_{i,c,k}P_{i,c,k,t}}}}$

With reference to the above equation, substantially uniform thermalefficiency,

_(i,c,k), relative to power consumption or transient environmentalconditions, including the temperature difference between the surroundingenvironment and zone 103 i, may be employed as a simplifying assumptionif the thermal efficiency of unit index k is relatively constant overthe observed operating conditions. Multi-modal HVAC units, includingheat pumps, may exhibit non-uniform thermal efficiency relative to powerconsumption, often demonstrating discontinuous or non-linear thermalefficiency over the observed operating conditions. In such environments,the thermal model as described, indirectly forms an aggregate estimateof thermal efficiency, extracted from specific observations.

A power estimate, P_(i,c,k,t), in zone 103 i, in cool state c, in unitindex k, at time t, presents a dilemma, as one or more units maydemonstrate similar thermal efficiency,

_(i,c,k). A simplifying assumption may define that power is consumed inone or more units which are aggregated into a primary unit, and thatremaining units are aggregated into one or more auxiliary unitrepresentations, due to similar anticipated efficiency. Alternatively,units may be prioritized, by relative efficiency or available capacity,and electively utilized to realize alternative temperature controlscenarios, while minimizing power consumption.

In some environments, power may not be directly observable ormeasurable, as a metered average of power consumed over a sample period,T_(S). In such systems, power can be abstracted to a normalizedrepresentation which defines a duty cycle, indirectly estimated fromrelay states. Independent of the source or units, power should generallybe normalized by the maximum available power to improve the numericalaccuracy of the solution.

The cool state c, which indicates if active cooling or active heating isenabled, implies independent estimation for thermal efficiency,

_(i,c,k), in unit index k, as active cooling and active heating may beperformed by physically different units. Even if the identical HVACunits are utilized to perform both active cooling and active heating, itis unreasonable to assume that these functions are performed withsimilar efficiency. Therefore, solutions must be independently formedand associated with a specific cooling state c, derived fromobservations exclusively constrained to either active cooling or activeheating operation.

Solar heat transfer,

${\frac{d}{dt}\left( Q_{{Si},t} \right)},$

to zone 103 i, from surface s, at time t, is equal to the aggregateproduct of thermal transmittance of surface s, h_(Si,s), a propertyrelated to the heat transfer characteristics of the surface material,the surface area of the shared boundary exposed to incident solarradiation, A_(Si,s), the complement of cloud cover, c_(i,t), defined asthe normalized ratio of solar irradiance obscured by clouds andavailable solar irradiance, I_(i,s,t), which is represented by thefollowing equation:

${\frac{d}{dt}\left( Q_{{Si},t} \right)} = {{\sum\limits_{s = 0}^{S - 1}\left( Q_{{Si},s,t} \right)} = {{\sum\limits_{s = 0}^{S - 1}{h_{{Si},s}{A_{{Si},s}\left( {1 - c_{i,t}} \right)}I_{i,s,t}}} \approx {h_{Si}A_{Si}I_{i,t}}}}$

As the relative geometry of zones within a site is unknown, and thegeometry and heat transfer characteristics of specific surfaces formingthe boundary to a zone i, is also unknown, it is impractical to directlycalculate the solar heat transfer for each surface s. The simplifyingassumptions of stationary geometry and boundary materials in zone i, anduniform cloud cover and incident solar irradiance relative to the zone,are useful and generally sufficient to simplify the solution. Solarirradiance incident upon and normal to a single aggregate surface, atthe location of the site, and accounting for losses due to cloud cover,may be readily provided by a weather service, further simplifying thesolution.

Unobserved heat transfer,

$\frac{d}{dt}\left( Q_{{Ui},t} \right)$

to zone 103 i, at time t, is equal to the unobserved heat, q_(i,t),which represents heat produced or transported by unknown, unmeasured, orunobservable sources, including fireplaces, ovens, stoves, lighting,non-instrumented HVAC units 104, or people, which is represented by thefollowing equation:

${\frac{d}{dt}\left( Q_{{Ui},t} \right)} = {q_{i,t} \approx q_{i}}$

Unobserved heat transfer,

${\frac{d}{dt}\left( Q_{{Ui},t} \right)},$

to zone 103 i may reasonably neglected if the unobserved heat is knownor determined to be negligible. Further, the simplifying assumption thatthe unobserved heat, q_(i), changes slowly with respect to time relativeto the memory depth, N, of the solution, and may be consideredquasi-stationary, is potentially useful or necessary to form awell-conditioned solution.

Heat transfer,

${\frac{d}{dt}\left( Q_{i,c,t} \right)},$

to zone 103 i, in cool state c, at time t, is generally not directlyobservable. The transformation from a continuous differential equationto an equivalent causal discrete-time difference equationrepresentation, and the substitution for neat transfer,

${\frac{d}{dt}\left( Q_{i,c,n} \right)},$

equal to the product of thermal mass, C_(i), and rate of temperaturechange,

${\frac{d}{dt}\left( T_{i,n} \right)},$

in zone i, at sample n, define a practical and useful relationship,which is represented by the following equation:

${\frac{d}{dt}\left( T_{i,n} \right)} = {{\left( \frac{1}{C_{i}} \right)\frac{d}{dn}\left( Q_{i,c,n} \right)} = {{\sum\limits_{\underset{j \neq i}{j = 0}}^{J}{\frac{h_{{Pi},j}A_{{Pi},j}}{C_{i}}\left( {T_{j,{n - 1}} - T_{i,{n - 1}}} \right)}} + {\sum\limits_{k = 0}^{K - 1}{\frac{\eta_{i,c,k}}{C_{i}}P_{i,c,k,n}}} + {\frac{h_{Si}A_{Si}}{C_{i}}I_{i,{n - 1}}} + \frac{q_{i}}{C_{i}}}}$

It is not necessary to explicitly determine several thermal systemproperties related to the rate of temperature change,

${\frac{d}{dt}\left( T_{i,n} \right)},$

including passive tnermal transmittance, h_(Pi,j), the surface area ofthe shared zone boundary, A_(Pi,j), thermal efficiency,

_(i,c,k), solar thermal transmittance, h_(Si), j, the surface area ofthe shared boundary exposed to incident solar radiation, A_(Si,s), andthermal mass, C_(i). Specific parameterized solutions, while potentiallyinteresting in a diagnostics context, are not necessary or useful tocharacterize heat transfer and exploit the observed relationship betweenenvironmental conditions, including temperature, and power consumption.

A thermal coefficient vector, w _(i,c,n), in zone 103 i, in cool statec, at sample n, abstracts system dependent characteristics from theabove equation, for notional convenience may be represented by thefollowing equation:

${\overset{\_}{\omega}}_{i,c,n} = \left\{ \begin{matrix}{\frac{h_{{Pi},j}A_{{Pi},j}}{C_{i}}\ } & {j{\text{:}\left\lbrack {0,{J - 1}} \right\rbrack}} \\\frac{\eta_{i,c,k,n}}{C_{i}} & {k{\text{:}\left\lbrack {0,{K - 1}} \right\rbrack}} \\\frac{h_{Si}A_{Si}}{C_{i}} & \; \\\frac{q_{i}}{C_{i}} & \;\end{matrix} \right.$

In some embodiments, the thermal coefficient vector, w _(i,c,n), in zone103 i, in cool state c, at sample n, includes thermal coefficientsrelated to passive heat transfer, indexed by zone j, of J zones whichmay share a boundary with zone i, active heat transfer, indexed by unitindex k, of K units, solar heat transfer, and an unobserved heattransfer. The passive thermal coefficients represent heat transfer fromzone j to zone i, eliminating the condition j=i, and including thesurrounding environment. Active thermal coefficients must beindependently evaluated in the context of active cooling or activeheating, which generally necessitates independent evaluations of thethermal coefficient vector, w _(i,c,n).

An incident vector, x _(i,c,n), in zone i, in cool state c, at sample n,in terms of temperature, T_(j,n-1), in zone j, at sample n-1,temperature, T_(i,n-1), in zone 103 i, power in unit index k,P_(i,c,k,n), and solar irradiance, I_(i,n-1), may be represented by thefollowing equation:

$x_{i,c,n}^{T}\left\{ \begin{matrix}\left( {T_{j,{n - 1}} - T_{i,{n - 1}}} \right. & {j{\text{:}\left\lbrack {0,{J - 1}} \right\rbrack}} \\P_{i,c,k,n} & {k{\text{:}\left\lbrack {0,{K - 1}} \right\rbrack}} \\I_{i,{n - 1}} & \; \\1 & \;\end{matrix} \right.$

With reference to the above equation, it is often useful to filter thepower, P_(i,c,k,n), in zone 103 i, in cool state c, in unit index k, atsample n, by applying an appropriate low pass filter. A representativepower filter is a Butterworth IIR filter, of order 2, with a −3 dBnormalized frequency equal to 0.2250790799, which has a nominal groupdelay of 2.0 samples. It is often convenient to normalize an incidentvector, x _(i,c,n), in zone i, in cool state c, at sample n, by scalingthe constituents to ensure that a common range is approximated,abstracting various units of measure. This technique may be useful forimproving numerical accuracy of the solution, and to indirectly scaleand normalize a thermal coefficient vector, w _(i,c,n), extracted in asolution. Representative normalization scales temperature difference by10° C., power by 1 kW, unless power is already normalized to a unityrange based on relay state, and solar irradiance by 1 kW/ m2, thoughalternative embodiments are viable and may be preferred.

A primary signal, y_(i,c,n), in zone 103 i, in cool state c, at samplen, is defined as the product of a sample period, T_(S), and an observedrate of temperature change,

${\frac{d}{dt}\left( T_{i,n} \right)},$

which may be calculated in various forms, including the first, second,and fourth order discrete derivatives defined, in terms of temperature,T_(i,n), previous temperature, T_(i,n-m), where m is in [1, 4], and isequal to the product of a thermal coefficient vector, w _(i,c,n), and anincident vector, x _(i,c,n), may be represented by the followingequation:

$y_{i,c,n} = {{{T_{S}\frac{d}{dn}\left( T_{i,n} \right)} \approx {T_{i,n} - T_{i,{n - 1}}} \approx \frac{T_{i,n} - T_{i,{n - 2}}}{2} \approx \frac{{- T_{i,n}} + {8T_{i,{n - 1}}} - {8T_{i,{n - 3}}} + T_{i,{n - 4}}}{12}} = {{\overset{¯}{x}}_{i,c,n}{\overset{¯}{\omega}}_{i,c,n}}}$

The selection of discrete derivative order is significant, as phase biasand latency compensation must be considered, and higher order discretederivative approximations may not be sufficiently compact relative tothe rate of temperature change,

${\frac{d}{dt}\left( T_{i,n} \right)},$

in zone 103 i, at sample n, and a sample period, T_(S). Derivativerepresentations are inherently noisy, as the process of differentiationeffectively amplifies high frequency noise content in the signal relatedto errors and uncertainty in observations. It is useful to filter aprimary signal, y_(i,c,n), in zone 103 i, in cool state c, at sample n,by applying an appropriate low pass filter. A representative primarysignal filter is a Butterworth IIR filter, of order 2, with a −3 dBnormalized frequency equal to 0.2250790799, which has a nominal groupdelay of 2.0 samples. The latency of each filter must be accounted forthrough application of latency compensation, which effectivelytemporally aligns constituents of a difference equation by insertingfilters or delays in appropriate signal paths, such that temporalalignment error related to asymmetric processing of specific signalpaths will be minimized, and a difference equation will be faithfullyimplemented. Latency compensation may take many forms, eitherintroducing delay to incident vector, x _(i,c,n), or primary signal,y_(i,c,n), associated with zone 103 i, in cool state c, at sample n,such that each path has equivalent aggregate delay.

In some embodiments, the thermal coefficient vector, w _(i,c,n), may beextracted from, and independently expressed in various forms, withsolutions including generalized linear inverse, or an adaptive filterbank. There are advantages associated with each solution, and anappropriate selection is application dependent. Generalized linearinverse and adaptive filter bank solutions are described, thoughalternative embodiments are viable and may be desired.

Generalized Linear Inverse

Generalized linear inverse, in some situations, is a statisticalsolution that can be applied to extract an estimate of a thermalcoefficient vector, w _(i,c,n), in zone i, in cool state c, at sample n,which minimizes the aggregate estimation error of a primary signal,y_(i,c,n), over a memory depth, N, corresponding to a set of independentobservations. A generalized linear inverse solution may be periodic, andobservations are not required to be sequentially ordered or contiguous.The solution is computationally intensive, relative to alternativemethods, yet is typically performed less frequently. Storagerequirements are proportional to a memory depth, N, and may besignificant. Numerical accuracy is largely dependent upon the diversityof observations and a memory depth, N. Changes in a dynamic thermalsystem may not be discernable at a temporal resolution significantlyless than a memory depth, N.

With respect to the generalized linear inverse solution, a primaryvector, y _(i,c,n), in zone 103 i, in cool state c, at sample n, isequal to the product of an incident matrix, X _(i,c,n), and a thermalcoefficient vector, w _(i,c,n). The primary vector, y _(i,c,n), andincident matrix, X _(i,c,n), have dimensions [N,1] and [N, J+K+2],respectively, in agreement with a thermal coefficient vector, w_(i,c,n), of dimension [J+K+2,1], over a memory depth, N, nominally 7days, may be represented by the following equation:

y _(i,c,n)=X _(i,c,n) ω _(i,c,n)

Each row of a primary vector, y _(i,c,n), and an incident matrix, X_(i,c,n), is formed from independent incident vector, x _(i,c,m), inzone i, and primary signal, y_(i,c,m), observations, where sample m isin [N-n, n], assuming synchronous and contiguous observation at a sampleperiod, T_(S). Order of observation over a memory depth, N, isindependent, and need not be contiguous or sequential. It isadvantageous to maximize the diversity of the observations, though theopportunity to do so may be constrained by a restriction to extractsolutions in environments employing entirely passive observation. Asolution may be formed with fewer observations, though a selection ofmemory depth, N, and diversity of observations largely determine thenumerical accuracy of a solution.

A thermal coefficient vector, w _(i,c,n), in zone i, in cool state c, atsample n, is a solution to a system of linear equations defined by anincident matrix X _(i,c,n), and a primary vector, y _(i,c,n), which maybe represented by the following equation:

ω _(i,c,n)=( X _(i,c,n) ^(T) X _(i,c,n))⁻¹ X _(i,c,n) ^(T) y _(i,c,n)

The thermal coefficient vector, w _(i,c,n), in zone i, in cool state c,at sample n, demonstrates numerical accuracy which is closely related tothe diversity or independence of observations in an incident matrix, X_(i,c,n), and a primary vector, y _(i,c,n). Diversity may be quantifiedby the condition number of the source matrix, X_(i,c,n) ^(T) X _(i,c,n),defined as the ratio of the maximum and minimum eigenvalues of thematrix. The condition number of a well-conditioned matrix approachesunity, and is infinite if the matrix is singular, and a solution is notpossible. The numerical accuracy of a thermal coefficient vector, w_(i,c,n), solution is dependent upon the diversity of the observationsfrom which it was formed, as the approximate digits of accuracy areproportional to the logarithm of the condition number. Explicitcomputation of the condition number prior to extracting a thermalcoefficient vector, w _(i,c,n), would significantly increase thecomputational complexity of the solution, and may not be practical orpossible in many environments. A practical and advantageous alternativemethod of rank reduction is defined, which dynamically tests andexcludes specific columns from an incident matrix, X _(i,c,n), andcorresponding thermal coefficient vector, w _(i,c,n), elements from asolution, ensuring sufficient diversity is present to form a solutionwith adequate numerical accuracy, when computation of a completesolution would otherwise not be possible, or useful.

Adaptive Filter Bank

In some implementations of the disclosure an filter bank 145 may beimplemented, which is an iterative solution applied to extract anestimate of coefficient and state vectors to indirectly approximate athermal coefficient vector, w _(i,c,n), in zone 103 i, in cool state c,at sample n. In turn, this minimizes the instantaneous estimation errorof a reference signal, v_(i,c,n), relative to an observed primarysignal, y_(i,c,n).

An adaptive filter bank solution is periodic, and observations arerequired to be sequentially ordered, though not contiguous. The solutionis not computationally intensive, relative to alternative methods, yetis typically performed more frequently, on each observation. Storagerequirements are minimal, and independent of the rate of convergence orthe effective memory depth. Numerical accuracy is largely dependent uponthe diversity of observations and the rate of adaptation, μ_(j). Changesin a dynamic thermal system are typically discernable at a temporalresolution which is significantly less than alternative methods,including generalized linear inverse. In some implementations, theadaptive filter bank 145 is constructed as a collection of J filters,each consuming an incident signal, x_(i,c,j,n), in zone i_(j) in coolstate c, in filter index j, at sample n, and producing a referencesignal, v_(i,c,j,n), where the effective transfer function of eachfilter is iteratively adapted as a function of a representation ofestimation error.

In this disclosure, the architecture of an Infinite Impulse Response(IIR) to a reference Direct II design, though alternative embodimentsincluding Direct I, Lattice, and Parallel are discussed and may bepreferred. A Finite Impulse Response (FIR) filter may be a viablealternative to an IIR filter, as it is architecturally equivalent, withthe additional restriction that a recursive coefficient vector,ā_(i,c,j,n), is static and comprised of elements with a value equal tozero. Adaptive filters with dynamic coefficients are described, thoughit may be advantageous to initially define one or more filters in anadaptive filter bank 145 with static coefficient, based on a prioriknowledge, or to transition to a static solution after achieving aspecified performance.

In some embodiments, the adaptive filter 200 is one in a collection ofadaptive filters that can make up an adaptive filter bank, such asadaptive filter bank 145 of FIG. 1. The system architecture 100 canimplement the adaptive filter bank 145 as processing logic 143 that caninclude hardware (e.g., circuitry, dedicated logic, programmable logic,microcode, etc.), software, firmware, or a combination thereof. In oneembodiment, the adaptive filter bank 145 can be implement as part of aservice in the cloud computing environment 105 of the system forcomfort-based management. For example, the service associated with theadaptive filter bank 145 can be utilized to adapt the thermal model 140to further assist in characterizing the heat transfer associated withthe comfort-based management of site 101. In other embodiments, theservice associated with the adaptive filter bank 145 may be installedand utilized for comfort-based management by various other components ofsystem architecture 100, which may or may not be geographicallydisbursed.

FIG. 2 is an example of an adaptive IIR filter 200 according to anembodiment of the disclosure in Direct II form. The adaptive filter 200implements a difference equation as a function of an incident signal210, x_(i,c,j,n), in zone 103 i, in cool state c, in filter index j, atsample n, a recursive coefficient vector 230, ā_(i,c,j,n), and a forwardcoefficient vector 240, b _(i,c,j,n), to produce a reference signal 220,v_(i,c,j,n). A state vector 250, s_(i,c,j,n), is implemented to retain arecursive internal filter state, and is delimited by discrete-time unitdelays 260, z⁻¹, and an filter order, M_(j). For example, the recursivecoefficient vector 230, ā_(i,c,j,n), forward coefficient vector 240, b_(i,c,j,n), and state vector 250, s_(i,c,j,n), in zone 103 i, in coolstate c, in filter index j, at sample n, are of dimension, [M_(j), 1].As a matter of notational convenience, a zero-index recursivecoefficient 230, ā_(i,c,j,0,n), has an implicit persistent value equalto zero, and a zero-index state coefficient, s_(i,c,j,0,n), consumes nostorage and is useful in the context of updating a state vector 250,s_(i,c,j,n).

In some embodiments, there are stability considerations in an adaptiveIIR filter 200, as poles, or roots of the denominator of a discretetransfer function derived from a z-transform of a difference equation,are constrained to the interior of a unit circle to form a stable causalsolution, and zeros, or roots of the numerator of the transfer function,may be similarly constrained only if a minimum phase solution isdesired. Root calculation may be computationally prohibitive in manyenvironments, though the process is dependent on filter order, M_(j).

In some embodiments, adaptive IIR filter 200 is initialized by assigninga stable recursive coefficient vector 230, ā_(i,c,j,0), in zone 103 i,in cool state c, in filter index j, at sample n equal to zero, withvalues determined from an a prior solution, or small random values, anda forward coefficient vector 240, b _(i,c,j,0), with values determinedfrom an a prior solution, or small random values.

A state coefficient 250, s_(i,c,j,m,0), in zone 103 i, in cool state c,in filter index j, in coefficient index m, at sample n, is initializedas a function of an initial incident signal 210, a recursive coefficientvector 230, ā_(i,c,j,0), and a forward coefficient vector 240, byassuming persistent operation in this condition to reduce edge effects,where m is in [1, M_(j)], which is represented by the followingequation:

${{s_{i,c,j,m,0} = {x_{i,c,j,0}\left( \frac{\left( {1 - b_{i,c,j,0,0}} \right)}{\sum\limits_{m = 1}^{M}\left( {{a_{i,c,j,m,0}b_{i,c,j,0,0}} + b_{i,c,j,m,0}} \right)} \right)}}}_{m:{\lbrack{1,M_{j}}\rbrack}}$

The adaptive IIR filter 200 is synchronously evaluated at a sampleperiod, T_(s), by defining a reference signal 220, v_(i,c,j,n), in zone103 i, in cool state c, in filter index j, at sample n, and modifying astate vector 250, s _(i,c,j,n). In one embodiment, the adaptive filter200 is electively adapted after each evaluation, by modifying arecursive coefficient vector 230, ā_(i,c,j,n), and a forward coefficientvector 240, b _(i,c,j,n). In this disclosure, the process by which thecoefficients of an adaptive filter are modified to Least Mean Squares(LMS) adaptation, though alternative embodiments including NormalizedLeast Mean Squares (NLMS), Recursive Least Squares (RLS), and othervariations of gradient descent adaptation are discussed and may bepreferred.

A reference signal 220, v_(i,c,j,n), in zone 103 i, in cool state c, infilter index j, at sample n, is equal to the sum of the product of thetranspose sum of a recursive coefficient vector 230, ā_(i,c,j,n), scaledby an initial forward coefficient 240, b _(i,c,j,0,n), and a forwardcoefficient vector 240, b _(i,c,j,n), and a state vector 250, s_(i,c,j,n), and the product of an incident signal 210, x_(i,c,j,n), andan initial forward coefficient, b_(i,c,j,0,n), which is represented bythe following equation:

${{v_{i,c,j,n} = {{\left( {{{\overset{\_}{a}}_{i,c,j,n}b_{i,c,j,0,n}} + {\overset{\_}{b}}_{i,c,j,n}} \right)^{T}{\overset{\_}{s}}_{i,c,j,n}} + {b_{i,c,j,0,n}x_{i,c,j,n}}}}}_{s_{i,c,j,0,n} = 0}$

With reference to the above equation, the state coefficient 250,s_(i,c,j,0,n), in zone 103 i, in cool state c, in filter index j, incoefficient index zero, at sample n, is the sum of the product of thetranspose of a recursive coefficient vector 230, ā_(i,c,j,n), and astate coefficient vector 250, s _(i,c,j,n), and an incident signal 210,x_(i,c,j,n), which is represented by the following equation:

s _(i,c,j,0,n) =ā _(i,c,j,n) ^(T) s _(i,c,j,n) +x _(i,c,j,n)

In some embodiments, the state coefficient 250, S_(i,c,j,m,n+1), in zone103 i, in cool state c, in filter index j, in coefficient index m, atsample n+1, is assigned the value of a state coefficient,s_(i,c,j,m,n l), in coefficient index m-1, at sample n, where m is in1[1,M_(j)], which is represented by the following equation:

s_(i, c, j, m, n + 1) = s_(i, c, j, m − 1, n)_(m : [1, M_(j)])

In some embodiments, a reference signal 220, v_(i,c,n), in zone 103 i,in cool state c, at sample n, is the sum of a reference signal 220,v_(i,c,j,n), in filter index j, in [0, J-1], which is represented by thefollowing equation:

$v_{i,c,n} = {\sum\limits_{j = 0}^{J - 1}v_{i,c,j,n}}$

In some embodiments, the estimation error, e_(i,c,n), in zone 103 i, incool state c, at sample n, is defined as the difference of a primarysignal, y_(i,c,n), and a reference signal, v_(i,c,n), and represents theerror associated with using a reference signal from an adaptive filterbank at a specific state to estimate a primary signal, which isrepresented by the following equation:

e _(ic,n) =y _(i,c,n) −v _(i,c,n)

The estimation error, e_(i,c,n), in zone 103 i, in cool state c, atsample n, is the instantaneous measure of the numerical accuracy of asolution, which is a necessary if not sufficient condition to adapt arecursive coefficient vector 230, ā_(i,c,j,n), and a forward coefficientvector 240, b _(i,c,j,n), in filter index j, in [0, J-1]. It may beuseful to visualize an estimation error, e_(i,c,n), as a contiguousdifferentiable surface in M_(j) dimensions, as a function of a recursivecoefficient vector 230 ā_(i,c,j,n), and a forward coefficient vector240, b _(i,c,j,n).

A recursive coefficient vector, ā_(i,c,j,n), in zone 103 i, in coolstate c, in filter index j, at sample n+1, is defined as the differenceof a recursive coefficient vector 230, ā_(i,j,n), at sample index n, andthe product of a rate of adaptation, μ_(j), and the gradient estimate ofa recursive coefficient, ∇a_(i,c,j,n), the partial derivative of an L₁or L₂ representation of estimation error, e² _(i,c,n), with respect torecursive coefficients, which is represented by the following equation:

${\overset{\_}{a}}_{i,c,j,{n + 1}} = {{{\overset{\_}{a}}_{i,c,j,n} - {\mu_{j}{\overset{\_}{\nabla}}_{a_{i,c,j,n}}}} = {{\overset{\_}{a}}_{i,c,j,n} - {\mu_{j}\left( {\frac{\partial}{\partial a_{i,c,j,n}}\left( e_{i,c,n}^{2} \right)} \right)}}}$

In the above note equation, the rate of adaptation, μ_(j), isexponentially related to the rate of convergence, and proportional tomisadjustment, or noise injected by the adaptive process, and must beselected appropriately to ensure a stable system with adequateconvergence and numerical accuracy, relative to the thermal system.

With reference to FIG. 2, a recursive coefficient vector 230,ā_(i,c,j,n+1), in zone 103 i, in cool state c, in filter index j, atsample n+1, is the sum of a recursive coefficient vector 230,ā_(i,c,j,n), at sample n, and the product of a rate of adaptation,μ_(j), an estimation error, e_(i,c,n), and the partial derivative of areference signal 220, v_(i,c,j,n), in filter index j, in [0, J-1], whichis represented by the following equation:

${\overset{\_}{a}}_{i,c,j,{n + 1}} = {{\overset{\_}{a}}_{i,c,j,n} - {\mu_{j}{e_{i,c,n}\left( {\frac{\partial}{\partial a_{i,c,j,n}}\left( v_{i,c,j,n} \right)} \right)}}}$

A state gradient vector, q _(i,c,j,n), in zone 103 i, in cool state c,in filter index j, at sample n, defined for notational convenience, isthe sum of the inner product of a recursive coefficient vector 230,ā_(i,c,j,n), and a state gradient vector, and a state gradient vector, q_(i,c,j,n), at sample index n-m, where m is in [1, M_(j)], which isrepresented by the following equation:

${{{\overset{\_}{q}}_{i,c,j,n} = {\left( {\frac{\partial}{\partial a_{i,c,j,n}}\left( {\overset{\_}{s}}_{i,c,j,n} \right)} \right) = {{{\overset{\_}{a}}_{i,c,j,{n - m}} \cdot {\overset{\_}{q}}_{i,c,j,{n - m}}} + {\overset{\_}{s}}_{i,c,j,{n - m}}}}}}_{m:{\lbrack{1,M_{j}}\rbrack}}$

With reference to the above equation, the recursive coefficient vector230, ā_(i,c,j,n+1), in zone 103 i, in cool state c, in filter index j,at sample n+1, is the sum of a recursive coefficient vector 230,ā_(i,c,j,n), at sample index n, and the product of a rate of adaptation,μ_(j), an estimation error, e_(i,c,n), and an expression of a recursivecoefficient vector 230, ā_(i,c,j,n), a forward coefficient vector 240, b_(i,c,j,n), and a state gradient vector, q _(i,c,j,n), which isrepresented by the following equation:

${\overset{\_}{a}}_{i,c,j,{n + 1}} = {{\overset{\_}{a}}_{i,c,j,n} + {\mu_{j}{e_{i,c,n}\left( {{b_{i,c,j,0,n}{\overset{\_}{s}}_{i,c,j,n}} + {\left( {{{\overset{\_}{a}}_{i,c,j,n}b_{i,c,j,0,n}} + {\overset{\_}{b}}_{i,c,j,n}} \right) \cdot {\overset{\_}{q}}_{i,c,j,n}}} \right)}_{\underset{s_{i,c,j,0,n} = 0}{q_{i,c,j,0,n} = 0}}}}$

In some embodiments, a forward coefficient vector 240, b _(i,c,j,n+1),in zone 130 i, in cool state c, in filter index j, at sample n+1, isdefined as the difference of a forward coefficient vector 240, b_(i,c,j,n), at sample index n, and the product of a rate of adaptation,μ_(j), and the gradient estimate of a recursive coefficient,∇b_(i,c,j,n), the partial derivative of an L₁ or L₂ representation ofestimation error, e² _(i,c,n), with respect to forward coefficients. Anequivalent expression is the sum of a forward coefficient vector 240, b_(i,c,j,n), at sample n, and the product of a rate of adaptation, μ_(j),an estimation error, e_(i,c,n), and the partial derivative of areference signal 220, v_(i,c,j,n), in filter index j, in [0, J-1], whichis represented by the following equation:

${\overset{\_}{b}}_{i,c,j,{n + 1}} = {{{\overset{\_}{b}}_{i,c,j,n} - {\mu_{j}\left( {\frac{\partial}{\partial b_{i,c,j,n}}\left( e_{i,c,n}^{2} \right)} \right)}} = {{\overset{\_}{b}}_{i,c,j,n} + {\mu_{j}{e_{i,c,n}\left( {\frac{\partial}{\partial b_{i,c,j,n}}\left( v_{i,c,j,n} \right)} \right)}}}}$

The forward coefficient, b_(i,c,j,0,n+1), in zone 103 i, in cool statec, in filter index j, in coefficient index zero, at sample n+1, is thesum of a forward coefficient, b_(i,c,j,0,n), at sample n, and theproduct of a rate of adaptation, μ_(j), an estimation error, e_(i,c,n),and the partial derivative of a reference signal 220, v_(i,c,j,n), infilter index j, in [0, J-1], which is represented by the followingequation:

b _(i,c,j,0,n+1) =b _(i,c,j,0,n) +μ _(j) e _(i,c,n)(ā _(i,c,j,n) ^(T) s_(i,c,j,n) +x _(i,c,j,n))

In other embodiments, the forward coefficient vector 240, b_(i,c,j,n+1), in zone 103 i, in cool state c, in filter index j, atsample n+1, is defined as the sum of a forward coefficient vector 240, b_(i,c,j,n), at sample index n, and the product of a rate of adaptation,μ_(j), an estimation error, e_(i,c,n), and a state vector, s_(i,c,j,n),which is represented by the following equation:

${\overset{\_}{b}}_{i,c,j,{n + 1}} = {{\overset{\_}{b}}_{i,c,j,n} + {\mu_{j}e_{i,c,n}{\overset{\_}{s}}_{i,c,j,n}_{s_{i,c,j,0,n} = 0}}}$

Turning to FIG. 3, an example architecture of an adaptive filter bank300 is shown. In some embodiments, the adaptive filter bank 300 may bethe same as adaptive filter bank 145 of FIG. 1. The adaptive filter bank300 may be constructed as a collection of adaptive filters 311-315, suchas the adaptive IIR filter 200 of FIG. 2.

A collection of adaptive filters 311-315 are defined to process anincident vector 310, x _(i,c,n), in zone i_(j), in cool state c, atsample n, with incident signals 210, x_(i,c,j,n), in filter index j,related to passive active, auxiliary, solar, and unobserved heattransfer. A reference signal 320, v_(i,c,n), is an aggregate estimate ofa primary signal 330, y_(i,c,n), after application of a suitable delay340, z^(−L), an application of latency compensation, which minimizestemporal alignment error by inserting a delay in a reference signal pathof L cycles. An estimation error 370, e_(i,c,n), is defined toelectively adapt recursive coefficient vectors, ā_(i,c,j,n), and forwardcoefficient vectors, b _(i,c,j,n), at various rates of adaptation,μ_(j).

Each adaptive filter 311-315 of the adaptive filter bank 300 consumes anincident vector 310, x _(i,c,n), in zone i, in cool state c, at samplen, with incident signals 210, x_(i,c,j,n), in filter index j, to producea reference signal 320, v_(i,c,n). For example, the incident signals210, x_(i,c,j,n), may be received from the thermal model 140 andincludes thermal coefficient data related to at least one of: an active,passive, solar irradiance and unobserved heat transfer in zones 103 i.In this regard, the adaptive filter bank 300 defines the thermalcoefficients associated with a corresponding heat transfer property sothat they can be individually evaluated and modified accordingly.

Each of the adaptive filters 311-315 of the adaptive filter bank 300includes a respective filter portion 311 p-315 p that is associated witha transfer function. An effective transfer function of the filterportions 311 p-315 p is iteratively adapted as a function of arepresentation of an estimation error 370, which represents the errorassociated with using the reference signal 230 from the adaptive filterbank 300 at a specific state to estimate a primary signal 340,y_(i,c,n). Each of the filter portions 311 p-315 p is defined to processthe incident vector 310, x _(i,c,n), in zone i, in cool state c, atsample n, with incident signals 210, x_(i,c,j,n), in filter index j,related to passive, active, auxiliary, solar, and unobserved heattransfer, to produce reference signal 320, v_(i,c,n). For example, thetransfer function may take a respective incident signal 210, x_(i,c,j,n)as input and return as output, a recursive coefficient vectorā_(i,c,j,n), a forward coefficient vector b _(i,c,j,n), and a rate ofadaptation, μ_(j),

In some embodiments, the reference signal 320, v_(i,c,n), is anaggregate of an estimate of a primary signal 330, y_(i,c,n) (which isproduced by each of the adaptive filters 311-315), after application ofa suitable delay, z^(L), (e.g., an application of latency compensation340). In one illustrative example, the latency compensation 340minimizes temporal alignment error by inserting a delay in a referencesignal path of L cycles (e.g., nominally in [0, 2]. The latency of eachof the adaptive filters 311-315 must be accounted for throughapplication of latency compensation 340, which effectively temporallyaligns constituents of a difference equation by inserting filters ordelays in appropriate signal paths. In this way, any temporal alignmenterror related to asymmetric processing of specific signal paths will beminimized, and a difference equation will be faithfully implemented.Latency compensation 340 may take many forms, for example, by eitherintroducing delay to incident vector 310, or primary signal 330,y_(i,c,n), associated with zone i, in cool state c, at sample n, suchthat each path has equivalent aggregate delay.

In some embodiments, the adaptive filters 311-315 of adaptive filterbank 300 may be adapted based on the estimation error 370, e_(i,c,n).For example, the estimation error 370, e_(i,c,n), is defined by theadaptive filter logic 132 to electively adapt recursive coefficientvectors, ā_(i,c,j,n), and forward coefficient vectors, b _(i,c,j,n), atvarious rates of adaptation, μ_(j). This is accomplished, for example,by the adaptive filter logic 132 utilizing the adaptive filters 311-315to solve a system of linear equations (as described with reference toadaptive filter 200 of FIG. 2), where each equation is formed from anindependent observation of the incident signals 210 associated with theincident vector 310 and a thermal coefficient vector w _(i,c,n). In someembodiments, the adaptive filters 311-315 are adaptively updated until asolution associated with zone 103 is satisfied. For example, thesolution may indicate a numerical convergence between the referencesignal 320 and the primary signal 330 associated with zone 103, whichhelps minimize estimation error and ensures the numerical accuracy of asolution for comfort-based management of zone 103.

FIG. 4 is an example graph 400 representing a thermal model adaptivefilter solution according to an embodiment of the disclosure. In FIG. 4,a recursive coefficient vector ā_(i,c,n), in zone i, in cool state c, atsample n, a forward coefficient vector, b _(i,c,n), is illustrated in acommercial site (e.g., site 101 of FIG. 1) with twelve zones,illustrating a specific zone (e.g., zone 103) containing five HVAC units(e.g., HVAC unit 104), at UTC-5, over consecutive days of activeheating. The recursive coefficient vector and forward coefficient vectorare associated with a thermal model (e.g., thermal model 140),implementing an adaptive filter bank solution in which the adaptivefilter bank 145 is initially reset to a nominal condition, and isiteratively adapted over an interval of contiguous operation.

In graph 400, a sequence of a reference signal, v_(i,c,n), estimatedfrom an adaptive filter bank which processes an incident vector, x_(i,c,n), and a primary signal, y_(i,c,n), calculated as a discrete rateof temperature change, an inherently noisy signal, are illustrated. Anestimation error, e_(i,c,n), defined as the difference between theprimary signal and reference signal, is employed to adapt the recursivecoefficient vector and forward coefficient vector, to continuously andopportunistically improve the reference signal estimate. Forwardcoefficient vector components associated with passive heat transfer,active heat transfer, and solar heat transfer are observed to exhibitsignificant change over 2019 Jan. 5 through 2019 Jan. 7, correspondingto significant changes in air temperature and solar irradiance outsidethe boundary of the thermal system, and corresponding increased powerconsumption in the zone. An increase in incident vector diversityreduced the estimation error, and the improved accuracy of the referencesignal estimation relative to the primary signal, illustrating thermalmodel convergence.

Estimation

In one illustrative example, the utility of a thermal model (e.g.,thermal model 140), and the justification for extracting and validatinga thermal coefficient vector, w _(i,c,n), is found in the estimation oftemperature and power, which facilitate applications including optimalstart, optimal stop, savings estimation, diagnostics, demand response,and virtual power plant capabilities. For example, a temperatureestimate, T_(i,n), in zone i, at sample n, is the sum of a previoustemperature, T_(i,n−1), at sample n−1, and a reference signal,v_(i,c,n), in an adaptive filter bank solution, is represented by thefollowing equation:

T _(i,n) =T _(i,n−1) +x _(i,c,n) ω _(i,c,n) =T _(i,n−1) +v _(i,c,n)

With reference to the above equation, the temperature estimation isuseful to iteratively estimate a sequence of temperatures, requiringonly a previous estimated or observed temperature, T_(i,n−1), a sequenceof anticipated power consumption vectors, P_(i,c,n), and forecasttemperature and solar irradiance estimates provided by a weather model,such as weather model 160 of FIG. 1. In some embodiment, the temperatureestimation may be used to project possible behavior relative to variousscenarios which differ in power consumption, availability, or cost.

A power estimate, P_(i,c,k,n), in zone 103 i, in cool state c, in unitindex k, at sample n, is the ratio of the difference of a primarysignal, y_(i,c,n), and the product of an incident vector, x _(i,c,n),and a thermal coefficient vector, w _(i,c,n), and an active thermalcoefficient, w _(i,c,m,n), in coefficient index m, assuming zero powerconsumption in associated unit k, may be represented by the followingequation.

$P_{i,c,k,n} = {\left( \frac{1}{\omega_{i,c,m,n}} \right)\left( {y_{i,c,n} - {{\overset{\_}{x}}_{i,c,n}{\overset{\_}{\omega}}_{i,c,n}}} \right)_{\underset{k\sim m}{P_{i,c,k,n} = 0}}}$

A specific solution for a power estimate, P_(i,c,k,n), in zone i, incool state c, in unit index k, at sample n, is not explicitly availablewithout a specific definition of the adaptive filters (such as adaptivefilters 311-315 of FIG. 3) used in an adaptive filter bank solution. Insome embodiments, the process for defining a solution for a powerestimate originates with a definition relating a reference signal,v_(i,c,j,n), in filter index j, associated with unit k, to an estimationerror, e_(i,c,n).

The reference signal, v_(i,c,j,n), in zone i, in cool state c, in filterindex j, at sample n, is the difference of a primary signal, y_(i,c,n),and a reference signal, v_(i,c,n), or equivalently an estimation error,e_(i,c,n), assuming zero power consumption in associated unit k, in anadaptive filter bank solution, which is represented by the followingequation:

$v_{i,c,j,n} = {{y_{i,c,n} - v_{i,c,n}} = {e_{i,c,n}_{\underset{k - j}{P_{i,c,k,n} = 0}}}}$

When an adaptive filter bank solution is comprised of adaptive IIRfilters, of filter order, M_(j), equal to zero. A recursive coefficientvector, ā_(i,c,j,n), in zone i, in cool state c, in filter index j, atsample n, is a vector of unit length with zero values. A forwardcoefficient vector, b _(i,c,j,n), in filter index j, is a vector of unitlength with an adaptive value equal a forward coefficient,b_(i,c,j,0,n), which is equivalent in representation to a thermalcoefficient, w _(i,c,m,n), in coefficient index m. A power estimate,P_(i,c,k,n), in this system is directly derived from the powerestimation equation above. In some embodiments, the power estimation isuseful to iteratively estimate a sequence of power consumption,requiring only a sequence of deterministic temperature estimates,T_(i,n), and forecast temperature and solar irradiance estimatesprovided by a weather model. The power estimation may also be used toproject possible behavior relative to alternative temperature controlscenarios.

If inter-zone passive heat transfer is electively considered in athermal system, such as site 101, estimation of temperature and powermust generally be performed recursively, through interaction with otherthermal models, as the passive heat transfer from each zone j which mayshare a boundary with zone 103 i will influence the temperature andpower consumption of zone 103 i. Alternatively, in many thermal systems,it may be either reasonable or practically necessary to assume thatinter-zone passive heat transfer is negligible relative to temperatureand power estimation. For example, it may be necessary to neglectinter-zone passive heat transfer in thermal systems where controltemperatures are similar in zones which share a boundary, as temperaturedifferences between the zones may not be sufficiently diverse to extractan accurate solution using the techniques disclosed herein.

Example Flow Diagrams

FIG. 5 is a flow diagram of a method 500 of implementing an adaptivefilter bank for modeling a thermal system according to an embodiment ofthe disclosure. Method 500 may be performed by processing logic that maycomprise hardware (e.g., circuitry, dedicated logic, programmable logic,microcode, etc.), software, firmware, or a combination thereof. In oneembodiment, the adaptive filter logic 125 as executed by a processor ofsystem architecture 100 may perform method 500. Although shown in aparticular sequence or order, unless otherwise specified, the order ofthe processes can be modified. Thus, the illustrated implementationsshould be understood only as examples, and the illustrated processes canbe performed in a different order, and some processes may be performedin parallel. Additionally, one or more processes can be omitted invarious embodiments. Thus, not all processes are required in everyimplementation. Other process flows are possible.

Method 500 begin in block 510 where an adaptive filter bank andassociated thermal coefficient data to characterize heat transfer of avolume of a thermal system are identified. For example, an adaptivefilter bank to define the architecture, order, and latency of componentfilters and associated thermal coefficients are identified tocharacterize heat transfer in a volume of a thermal system. In block520, reference signal data indicating an estimate of a rate oftemperature change in the volume based on at least the adaptive filterbank is generated. In block 530, primary signal data based at least onan observed rate of temperature change in the volume is received. Anestimation error for the reference signal data with respect to theprimary signal data associated with the volume is determined in block540. In view of the estimation error, the thermal coefficient data ismodified in block 550 to satisfy a solution associated with the volume.For example, the thermal coefficients are modified to reduce estimationerror and improve approximation of a rate of temperature change in areference signal.

FIG. 6 is a flow diagram of another method 600 of implementing anadaptive filter for modeling a thermal system according to an embodimentof the disclosure. Method 600 may be performed by processing logic thatmay comprise hardware (e.g., circuitry, dedicated logic, programmablelogic, microcode, etc.), software, firmware, or a combination thereof.In one embodiment, the adaptive filter logic 125 as executed by aprocessor of system architecture 100 may perform method 600. Althoughshown in a particular sequence or order, unless otherwise specified, theorder of the processes can be modified. Thus, the illustratedimplementations should be understood only as examples, and theillustrated processes can be performed in a different order, and someprocesses may be performed in parallel. Additionally, one or moreprocesses can be omitted in various embodiments. Thus, not all processesare required in every implementation. Other process flows are possible.

Method 600 begin in block 610 where an incident signal comprisingthermal coefficients associated with a volume of a thermal system isreceived at an adaptive filter bank. In block 620, a reference signalindicating an estimate of a rate of temperature change in the volumebased on at least the adaptive filter bank is produced. An estimationerror for the reference signal with respect to a primary signalassociated with the volume is determined in block 630. The adaptivefilter bank is updated in block 640 based on the estimation error tomeet an approximation of the rate of temperature change in the volumewith respect to a reference signal.

Diagnostics

Turning to FIG. 7, a flow diagram of a method 700 of using an adaptivefilter bank (e.g., adaptive filter bank 145) to detect diagnostic eventsin a thermal system, such as site 103 of FIG. 1, is shown. For example,the method 700 defines diagnostics events in a diagnostic model 701 todetect a change in state of representation (e.g., adapt thermal model702) of the thermal system 103 over various time intervals, which mayindicate anomalous operations. Method 700 may be performed by processinglogic that may comprise hardware (e.g., circuitry, dedicated logic,programmable logic, microcode, etc.), software, firmware, or acombination thereof. In one embodiment, the adaptive filter bank logic155 as executed by a processor of system architecture 100 may performmethod 700. Although shown in a particular sequence or order, unlessotherwise specified, the order of the processes can be modified. Thus,the illustrated implementations should be understood only as examples,and the illustrated processes can be performed in a different order, andsome processes may be performed in parallel. Additionally, one or moreprocesses can be omitted in various embodiments. Thus, not all processesare required in every implementation. Other process flows are possible.

In this example, diagnostics provides information related to thecondition of a thermal system, such as site 101. The diagnostics may bebased on an analysis of characteristics of a dynamic representation ofthe thermal system 101. In that regard, diagnostics events may bedescribed as transient or persistent, and defined from continuousmonitoring, local analysis, or aggregate analysis of independent thermalsystems with similar design, construction or geography. The diagnosticevents may indicate detection of a change in observed or estimatedcharacteristics of the thermal system 101 which may be related todefective or anomalous operation. Absent independent means to examine athermal system, the correlation between detection of a diagnostic eventand either the presence or cause of anomalous operation cannot beconfirmed. In this context, the purpose of diagnostics method 700 is todetermine if a thermal system is operating in a manner which isinconsistent with normal or anticipated behavior.

In some embodiments, the diagnostic events may be generated due toevaluation of observations and estimates, over various time intervalswhich support classification as, for example, transient or persistent.These classifications are not exclusive or unique, as transientdiagnostic events may eventually become persistent, and cyclic orquasi-periodic diagnostic events are plausible in many environments.Diagnostic evaluation over various time intervals is of practicalutility, as anomalous operation may evolve over different timeintervals, from seconds to months in duration. In some examples, a modeof operation of thermal devices 150 of the thermal system 101 that maycause a transient diagnostic event detection includes pump, valve, orrelay failure, in hydronic heating systems, or relay failure or rapidrefrigerant leaks in air-based furnace, heat pump, or air conditioningsystems. In other examples, a mode of operation of the thermal devices150 that may cause a persistent diagnostic event detection include slowboiler, pipe, or radiator water leaks, or sludge accumulation due tooxidization, in hydronic systems, or slow refrigerant leaks, damagedheat exchangers, or contaminated ducts and filters in air-based systems.A transient diagnostic event may demonstrate either cyclic orquasi-periodic or persistent behavior, which may be caused by conditionsincluding a slow water leak in a hydronic system, as an occupant mayeither be aware of the defect and elect to occasionally replace waterand restore normal operations or allow the defect to evolve intopersistent and increasingly anomalous operation.

With reference to the diagnostic model 701 of FIG. 7, the diagnosticsdetect a change in state of a representation of a thermal system whichmay indicate anomalous operation. A dynamic representation of the stateof a thermal system, including a physical or abstract thermal model, isminimally sufficient and necessary to facilitate diagnostics.

A representative thermal model appropriate for application indiagnostics includes a physical thermal model described by the followingheat transfer difference equation:

${\frac{d}{dn}\left( T_{i,n} \right)} = {{\left( \frac{1}{C_{i}} \right)\frac{d}{dn}\left( Q_{i,c,n} \right)} = {{\sum\limits_{\underset{j \neq i}{j = 0}}^{J}{\frac{h_{{Pi},j}A_{{Pi},j}}{C_{i}}\left( {T_{j,{n - 1}} - T_{i,{n - 1}}} \right)}} + {\sum\limits_{k = 0}^{K - 1}{\frac{\eta_{i,c,k}}{C_{i}}P_{i,c,k,n}}} + {\frac{h_{Si}A_{Si}}{C_{i}}I_{i,{n - 1}}} + \frac{q_{i}}{C_{i}}}}$

The heat transfer difference equation above defines a physicalrelationship which relates the rate of temperature change,

${\frac{d}{dt}\left( T_{i,n} \right)},$

in zone 103 i, at sample n, to observations and estimates, from which aconvenient thermal coefficient vector, w _(i,c,n), in cool state c. Inthis context, a thermal coefficient vector is a dynamic physicalrepresentation of the state of a specific zone in a thermal system, asthe constituents conveniently define normalized rates of passive,active, solar, and unobserved heat transfer, as disclosed herein.

In a typical site (such as site 101), a passive heat transfercoefficient, w _(p,i,n), in zone 103 i, at sample n, is relativelystationary, as it is related to the geometry and material propertiesassociated with a specific zone relative to a temperature differential.In this regard, an active heat transfer coefficient, w _(a,i,c,n), incool state c, is proportional to the efficiency, η_(i,c,n), of an HVACunit, and dynamic based on varying environmental conditions or design,in systems including heat pumps, multi-modal systems, and systems withvariable compressor speed, or it may change due to anomalous operation.A solar heat transfer coefficient, w _(s,i,n), is relatively stationary,as it is related to the geometry and material properties associated witha specific zone relative to incident solar energy. An unobserved heattransfer coefficient, w _(u,i,n), is relatively stationary, as it istypically aggregated over a sufficient duration of time to satisfy thissimplifying assumption.

In some embodiments, continuous monitoring may opportunistically orperiodically evaluate a solution for observation and control of athermal system to ensure that installation, configuration, and operationare consistent with expected behavior. A diagnostic event may be definedif communications with one or more thermal devices or cloud-basedresources, including a thread, worker role, remote computing node,virtual machine, cache, table, dictionary, database, data lake, hub, orservice is inaccessible or demonstrates anomalous operation, includingexcess latency or data corruption. Continuous monitoring may be realizedas a supervisory agent with sufficient visibility and access intocomponents of a solution which are essential to ensure that observationsand estimates are defined and retained with sufficient quality,quantity, and density to facilitate local and aggregate analysis.

Turning back to FIG. 7, method 700 begins in blocks 710-730 where for aspecific site 101, a thermal model, such as thermal model 140, isconstructed, initialized, and adapted (e.g., using adaptive filter bank145 of FIG. 1) on a per zone (e.g., zone 103) basis. In someembodiments, a representative thermal model appropriate for applicationin diagnostics include a physical thermal model described by a heattransfer difference equation as described herein. Each adaptive processper zone, produces dynamic estimate of thermal coefficient vectors, w_(i,c,n), in zone 103 i, in cool state c, at sample n, which may be usedto describe and estimate the behavior of the thermal system 101. Inblock 750, the thermal model data that includes the thermal coefficientvectors is feed to the diagnostic model 701.

In block 740, one or more filters are applied to the thermal coefficientdata based on a sampling rate. For example, the diagnostic model 701 isutilized to electively filter thermal coefficient vectors, w _(i,c,n),in zone 103 i, in cool state c, at sample n, by applying a collection oflinear or nonlinear filters. This in tuns may include morphologicaloperators to reduce noise and volatility while preserving features. Inblock 750, the sampling rate may be adapted and electively combined withfilter operations to reduce aliasing and implement rate adaptation,converting thermal coefficient vectors, w _(i,c,n), with a sampleperiod, T_(S) (e.g., nominally 600-900 seconds), to an effective sampleperiod (e.g., nominally 24 hours). In some embodiments, therepresentative filter operations include a Butterworth IIR filter, oforder 2, with a −3 dB normalized frequency, ƒ_(c), less than or equal to

$\frac{Ts}{24*3600},$

which has a nominal group delay of ƒ_(c) ⁻¹ samples, which may beefficiently integrated with a decimation filter to achieve an effectivesample period.

In block 760, one or more estimate thermal coefficient thresholds aregenerated in response to responsive to the applying the filters. Forexample, the diagnostic model 701 is utilized to estimate thermalcoefficient thresholds, ā_(i,c,n), in zone 103 i, in cool state c, atsample n, over a contiguous interval with a memory depth, N, or windowlength. This is accomplished by evaluating a sequence of thermalcoefficient vectors, w _(i,c,n), after application of a filter and rateadaptation operations, to determine if a trend or pattern of behavior isobserved that is sufficient to support the definition of a diagnosticevent. Thermal coefficient thresholds, ā_(i,c,n), are defined throughapplication of linear or nonlinear operations on thermal coefficientsconstrained to a specific window, where each successive window shares[0, N-1] samples with a previous window. This is conducted to determineif the thermal model 140 has demonstrated convergence to a solution witha minimal estimation error over a specific window, and at a minimum theboundary samples of a window, with sufficient confidence to justifyestimation of thermal coefficient thresholds, ā_(i,c,n), in zone 103 i,in cool state c, at sample n. If the thermal model 140 has notsufficiently converged over a window, it may not be plausible toidentify a diagnostic event over the corresponding interval.

In block 770, the thermal coefficient data is evaluated to determine ifany satisfies a corresponding estimated thermal coefficient threshold.In one illustrative example, the diagnostic model 710 is utilized toevaluate an active heat transfer coefficient, |w _(a,i,c,n)|, in zone103 i, in cool state c, at sample n, of thermal coefficient vector, w_(i,c,n), bounding a specific window to determine if the coefficientadaptation demonstrates sufficient change to indicate an effective lossin efficiency,

_(i,c,n), which exceeds a normalized efficiency threshold, ε_(a,c)(e.g., nominally 0.025 per day reduction in magnitude). The efficiencythreshold, ε_(a,c), significantly affects the sensitivity of detectionof diagnostic events, and may be determined empirically, based at leastin part on the geometry, geography, materials, construction, and HVACunit types typical of sites in a region.

Estimation of a probability density function, P_(a,i,c,n), in zone 103i, in cool state c, at sample n, with a memory depth N, of an activeheat transfer coefficient, |w _(a,ic,n)|, of thermal coefficient vector,w _(i,c,n), can extract first and third quartile estimates of theassociated probability distribution function, P_(a,i,c,n), forapplication as thermal coefficient thresholds, ā_(i,c,n). The evaluationof an active heat transfer coefficient, |w _(a,i,c,n)|, in zone 103 i,in cool state c, at sample n, of thermal coefficient vector, w_(a,i,c,n)|, bounding a specific window is done to determine if theactive heat transfer coefficient, |w _(a,i,c,n)|, is less than or equalto _(min)(ā_(i,c,n)), and the active heat transfer coefficient, |w_(a,i,c,n-N+1)|, is greater than or equal to _(max)(ā_(i,c,n)). Further,it may be useful to assert that the active heat transfer coefficient, |w_(a,i,c,n-2N+1)|, is also greater than or to _(max) (ā_(i,c,n)), toincrease confidence that an observed reduction in efficiency,

_(i,c,n), forms a pattern or trend consistent with contiguous loss. Asthe rate of reduction in efficiency,

_(i,c,n), is dependent upon the mode of operation which may causetransient or persistent diagnostic event detection, there isconsiderable utility in diagnostic model evaluation at various memorydepths.

An additional elective restrictions may be applied to the evaluation ofa sequence of thermal coefficient vector, w _(i,c,n), with a memorydepth, N, including determination that a passive heat transfercoefficient, w_(p,i,c,n), or a solar heat transfer coefficient,w_(s,i,c,n), are statistically proximate to expected values, or that anunobserved heat transfer coefficient, |w_(u,i,c,n)|, may be consideredto be insignificant relative to other means of heat transfer.

In block 780, alert information indicative of a diagnostic eventassociated with the thermal system may be generated based on theevaluation of the thresholds. For example, a diagnostic event may beidentified if any of the thermal coefficients, w_(i,c,n), are found tosatisfy defined constraints and demonstrate anomalous operation over acontiguous interval with a memory depth, N. The alert information may beindicative of, for example, a transient diagnostic event detection thatmay include pump, valve, or relay failures, in hydronic heating systems,or relay failure or rapid refrigerant leaks in air-based furnace, heatpump, or air conditioning systems, a persistent diagnostic eventdetection that may include slow boiler, pipe, or radiator water leaks,or sludge accumulation due to oxidization, in hydronic systems, or slowrefrigerant leaks, damaged heat exchangers, or contaminated ducts andfilters in air-based systems, or other types of detected diagnosticevents.

Diagnostic Events Detection Examples

FIGS. 8A-8D are example graphs 800, 820, 840 and 860 illustratingdiagnostic event data according to an embodiment of the disclosure.

In FIG, 8A, graph 800 illiterates using plot points 802 an active heattransfer coefficient, w_(a,i,c,n), in zone i, in cool state c, at samplen, and a thermal model temperature estimation error, e_(i,n), for a sitewith one observable zone, at UTC, in the U.K., over 45 days of activeheating in a hydronic system. A diagnostic event is detected using thetechniques disclosed herein at 2017 Mar. 26 plot point 808, with atransient local classification based on a memory depth, N, equal to 3days, in dark shading 804. It should be noted that the trend in implicitcontiguous reduction in efficiency,

_(i,c,n), was also observed over an interval of twice the memory depth,N, equal to 6 days, in light shading 806. In this analysis, aconservative normalized efficiency threshold, ε_(a,c), equal to 0.05 wasapplied. In a collection of 1872 sites, each with one observable zone,distributed across the U.K., over two consecutive months of hydronicheating, at least one transient local diagnostic event was detected in38 sites. Effectively 2.03% of the sites in the collection wereidentified through diagnostic analysis (e.g., utilizing method 700 ofFIG. 7) as demonstrating transient anomalous operation.

In FIG. 8B, graph 820 illiterates using plot points 822 an active heattransfer coefficient, w_(a,i,c,n), in zone i, in cool state c, at samplen, and a thermal model temperature estimation error, e_(i,n), for a sitewith one observable zone, at UTC, in the U.K., over 45 days of activeheating in a hydronic system. A sequence of diagnostic events isdetected using the techniques disclosed herein at 2017 Apr. 11 plotpoint 824, 2017 Apr. 12 plot point 825, 2017 Apr. 13 plot point 826, and2017 Apr. 14 plot point 828, with a persistent local classificationbased on a memory depth, N, equal to 14 days, in dark shading 829. Itshould be noted that the trend in implicit contiguous reduction inefficiency,

_(i,c,n), was also observed over an interval of twice the memory depth,N, equal to 28 days, in light shading 827. In this analysis, aconservative normalized efficiency threshold, ε_(a,c), equal to 0.025was applied. In a collection of 1872 sites, each with one observablezone, distributed across the U.K., over two consecutive months ofhydronic heating, at least one persistent local diagnostic event wasdetected in 96 sites. Effectively 5.13% of the sites in the collectionwere identified through diagnostic analysis as demonstrating persistentanomalous operation.

In some embodiments, the diagnostic events 824, 825, 826, 828 may beuniquely identified or validated with improved confidence throughaggregate analysis. The aggregate analysis may consider trends orstatistical metrics across a collection of sites and may select sitesfor inclusion based on factors including similar age, geometry,geography, construction, weather, HVAC unit type, energy consumption,population density or occupant demographics. In some embodiments, theprobability density functions may be estimated for properties ofinterest, including thermal coefficients, for a collection of sites, toand persistent aggregate diagnostic events may be independentlyidentified in sites which demonstrate anomalous behavior relative tostatistical norms. For example, sites with zones in which associatedthermal models have converged to solutions with a passive heat transfercoefficient, w_(p,i,n), or solar heat transfer coefficient, w_(s,i,n),in zone i, at sample n, above a threshold, nominally in the 90thpercentile of a probability distribution, may define persistentaggregate diagnostic events indicative of relatively poor insulation ormaterials which exceed a reporting threshold for anomalous operation.Similarly, an active heat transfer coefficients, w_(a,i,c,n), below athreshold, nominally the 10th percentile of a probability distributionmay define persistent aggregate diagnostic events indicative ofrelatively poor HVAC unit efficiency,

_(i,c,n).

In FIG. 8C, a series of probability density functions, P_(k,n), forcondition k in {w_(p,n), w_(a,n), e_(n)}, at sample n, are illustratedin graph 840 at plot points 842, 844, and 846 for a collection of 1872sites, each with one observable zone, at UTC, in the U.K., over twoconsecutive months of active heating in independent hydronic systems. Inthis example, quartiles are delimited by vertical lines 845, which boundthe middle 50th percentile of the respective probability distributions,in dark shading 843. For example, an active heat transfer coefficient,w_(a,n), has a probability distribution with a 25th percentile of 0.14,a 50th percentile of 0.19, and a 75th percentile of 0.275. In someembodiments, aggregate analysis may also estimate the rate of change ofa metric of interest and normalize an associated metric calculated inlocal analysis. This may improve the confidence of diagnostic eventdetection using the techniques of method 700 of FIG. 7 and account forerrors that may not be directly observable in a single site. Rather,they may be readily detectable and statistically significant when formedover a collection of sites.

In FIG. 8D, graph 860 illustrates using plot points 862 a probabilitydensity function, P_(ΔWa,n), for a relative change in an active heattransfer coefficient, Δw_(a,n), at sample n, for a collection of 1872sites, each with one observable zone, at UTC, in the U.K., over twoconsecutive months of active heating in independent hydronic systems. Inthis example, quartiles are delimited by vertical lines 863, which boundthe middle 50th percentile of the respective probability distributions,in dark shading 864. The relative change in an active heat transfercoefficient, Δw_(a,n), has a probability distribution with a 25thpercentile of −0.05, a 50th percentile of −0.02, and a 75th percentileof 0.005. Here, aggregate analysis may improve the confidence in a localdiagnostic event detection, by estimating the expectation of relativechange in an active heat transfer coefficient,

_(i,c,n), across a collection of sites, and normalizing the resultsobtained in the local analysis illustrated in graph 860 of FIG. 8D.

In some embodiments, the results may be normalized to account forpotential sources of error, which may include forecast weatherestimates, thermal device observations, or significant unobserved heattransfer potentially due to the presence of additional controlled andunobserved zones. In this example, a relative change in active heattransfer coefficient, Δw_(a,n), has an expected value equal to −0.02,for a typical or median site, over the two consecutive months ofinterest. Therefore, a normalized efficiency threshold, ε_(a,c), equalto 0.025, may be adjusted to account for the aggregate anticipated lossof efficiency, equal to 0.0253 in this example. Alternatively, a thermalcoefficient, {acute over (w)}_(i,c,n), or a relative change in a thermalcoefficient, Δw _(i,c,n), may be normalized to account for any observedaggregate change.

Controller Device

FIG. 9 is a block diagram illustrating a machine 900 in the form of aninterior volume thermal modeling and control device (hereinafter “IVTMCcontroller”) 901 that can learn from a set of weather estimations andthermal properties to predict and control energy consumption, powerconsumption and/or temperatures associated to one or more volumes orenclosed environments of a thermal system. In some embodiments, themachine 900 may represent a computer system within which a set ofinstructions 935, for causing the machine 900 to perform any one or moreof the methodologies discussed herein, may be executed. In variousillustrative examples, the IVTMC controller 901 may correspond to acomputing node 107 of the system 100 of FIG. 1. For example, the IVTMCcontroller 901 may include instructions implementing the adaptive filterbank 145 for modeling a thermal system, such as site 101 of FIG. 1.

The IVTMC controller 901 may be based on computer that may include, butare not limited to, components such as: a computer systemization 902connected to memory 929. In one embodiment, the IVTMC controller 901 maybe connected to and/or communicate with entities such as, but notlimited to: one or more users 933a from user input devices 911;peripheral devices 912; an optional cryptographic processor device 926;and/or a communications network 913, such as Local Area Networks (LANs),Pico networks, Wide Area Networks (WANs), Wireless Networks (WLANs), anintranet, an extranet, the Internet, etc.

Computer systemization 902 may comprise a clock 930, central processingunit (“CPU(s)” and/or “processor(s)” (these terms are usedinterchangeable throughout the disclosure unless noted to the contrary))903, a memory 929 (e.g., a read only memory (ROM) 906, a random accessmemory (RAM) 905, etc.), and/or an interface bus 907, and mostfrequently, although not necessarily, are all interconnected and/orcommunicating through a system bus 904 on one or more (mother)board(s)having conductive and/or otherwise transportive circuit pathways throughwhich instructions (e.g., binary encoded signals) may travel toeffectuate communications, operations, storage, etc. The computersystemization may be connected to a power source 926; e.g., optionallythe power source may be internal. Optionally, a cryptographic processor926 and/or transceivers (e.g., ICs) 974 may be connected to the systembus. In another embodiment, the cryptographic processor and/ortransceivers may be connected as either internal and/or externalperipheral devices 912 via the interface bus I/O. In turn, thetransceivers may be connected to antenna(s) 975, thereby effectuatingwireless transmission and reception of various communication and/orsensor protocols.

The power source 926 may be of any standard form for powering smallelectronic circuit board devices such as the following power cells:alkaline, lithium hydride, lithium ion, lithium polymer, nickel cadmium,solar cells, and/or the like. Other types of AC or DC power sources maybe used as well. In the case of solar cells, in one embodiment, the caseprovides an aperture through which the solar cell may capture photonicenergy. The power source 926 is connected to at least one of theinterconnected subsequent components of the IVTMC thereby providing anelectric current to all subsequent components. In an alternativeembodiment, an outside power source 926 is provided through a connectionacross the I/O 908 interface. For example, a USB and/or IEEE 1394connection carries both data and power across the connection and istherefore a suitable source of power.

Interface bus(es) 907 may accept, connect, and/or communicate to anumber of interface adapters, conventionally although not necessarily inthe form of adapter cards, such as but not limited to: input outputinterfaces (I/O) 908, storage interfaces 909, network interfaces 910,and/or the like. Optionally, cryptographic processor interfaces 927similarly may be connected to the interface bus. The interface busprovides for the communications of interface adapters with one anotheras well as with other components of the computer systemization.

Storage interfaces 909 may accept, communicate, and/or connect to anumber of storage devices such as, but not limited to: storage devices914, removable disc devices, and/or the like. Storage interfaces mayemploy connection protocols such as, but not limited to: (Ultra)(Serial) Advanced Technology Attachment (Packet Interface) ((Ultra)(Serial) ATA(PI)), (Enhanced) Integrated Drive Electronics ((E)IDE),Institute of Electrical and Electronics Engineers (IEEE) 1394, fiberchannel, Small Computer Systems Interface (SCSI), Universal Serial Bus(USB), and/or the like.

Network interfaces 910 may accept, communicate, and/or connect to acommunications network 913. Through a communications network 913, theIVTMC controller 901 is accessible through remote clients 933b (e.g.,computers with web browsers) by users 933a a. Network interfaces mayemploy connection protocols such as, but not limited to: direct connect,Ethernet (thick, thin, twisted pair 10/100/1000 Base T, and/or thelike), Token Ring, wireless connection such as IEEE 802.11 a-x, and/orthe like. Should processing requirements dictate a greater amount speedand/or capacity, distributed network controllers (e.g., DistributedIVTMC), architectures may similarly be employed to pool, load balance,and/or otherwise increase the communicative bandwidth required by theIVTMC controller 901. Further, multiple network interfaces 910 may beused to engage with various communications network 913 types. Forexample, multiple network interfaces may be employed to allow for thecommunication over broadcast, multicast, and/or unicast networks.

The Input/Output interfaces (I/O) 908 may accept, communicate, and/orconnect to user input devices 911, peripheral devices 912, cryptographicprocessor devices 926, and/or the like. I/O may employ connectionprotocols such as, but not limited to: audio: analog, digital, monaural,RCA, stereo, and/or the like. User input devices 911 often are a type ofperipheral device and may include: card readers, dongles, finger printreaders, gloves, graphics tablets, joysticks, keyboards, microphones,mouse (mice), remote controls, retina readers, touch screens (e.g.,capacitive, resistive, etc.), trackballs, trackpads, sensors (e.g.,accelerometers, ambient light, GPS, gyroscopes, proximity, etc.),styluses, and/or the like.

Generally, any mechanization and/or embodiment allowing a processor toaffect the storage and/or retrieval of information is regarded as memory929. However, memory is a fungible technology and resource, thus, anynumber of memory embodiments may be employed in lieu of or in concertwith one another. It is to be understood that the IVTMC controller 901and/or a computer systemization may employ various forms of memory 929.For example, a computer systemization may be configured wherein theoperation of on-chip CPU memory (e.g., registers), RAM, ROM, and anyother storage devices are provided by a paper punch tape or paper punchcard mechanism; however, such an embodiment would result in an extremelyslow rate of operation. In a typical configuration, memory 929 willinclude ROM 906, RAM 905, and a storage device 914. A storage device 914may be any conventional computer system storage. Storage devices mayinclude a computer-readable storage medium 935; a drum; a (fixed and/orremovable) magnetic disk drive; a magneto-optical drive; an opticaldrive (i.e., Blueray, CD ROM/RAM/Recordable (R)/ReWritable (RW), DVDR/RW, HD DVD R/RW etc.); an array of devices (e.g., Redundant Array ofIndependent Disks (RAID)); solid state memory devices (USB memory, solidstate drives (SSD), etc.); other processor-readable storage mediums;and/or other devices of the like. Thus, a computer systemizationgenerally requires and makes use of memory.

While a non-transitory computer-readable storage medium 935 is shown inthe illustrative examples as a single medium, the term“computer-readable storage medium” shall include a single medium ormultiple medium (e.g., a centralized or distributed database, and/orassociated caches and servers) that store the one or more sets ofexecutable instructions. The term “computer-readable storage medium”shall also include any tangible medium that is capable of storing orencoding a set of instructions for execution by a computer that causethe computer to perform any one or more of the methods described herein.The term “computer-readable storage medium” shall include, but not belimited to, solid-state memories, optical media, and magnetic media. Thenon-transitory computer-readable storage medium 935 on which may includeinstructions encoding any one or more of the methods or functionsdescribed herein, including instructions implementing the adaptivefilter bank 145 of FIG. 1 for implementing method 500 of FIG. 5, method600 of FIG. 6 and method 700 of FIG. 7 as disclosed herein. Anycomponent may be stored and accessed from the storage devices and/orfrom storage devices accessible through an interface bus. Althoughprogram components such as those in the component collection, typically,are stored in a local storage device 935, they may also be loaded and/orstored in other memory such as: remote “cloud” storage facilitiesaccessible through a communications network; integrated ROM memory 906;via an FPGA or ASIC implementing component logic; and/or the like.

The memory 929 may contain a collection of program and/or databasecomponents and/or data such as, but not limited to: operating systemcomponent 915; information server component 916; user interfacecomponent 917; database component 920; cryptographic server component918; IVTMC Component 919; and/or the like (i.e., collectively acomponent collection). The aforementioned components may be incorporatedinto (e.g., be sub-components of), loaded from, loaded by, or otherwiseoperatively available to and from the IVTMC component(s) 919.

The operating system component 915 is an executable program componentfacilitating the operation of the IVTMC controller 901. Typically, theoperating system facilitates access of I/O, network interfaces,peripheral devices, storage devices, and/or the like. The operatingsystem may be a highly fault tolerant, scalable, and secure system suchas: Unix and Unix-like system distributions (such as AT&T's UNIX;Berkley Software Distribution (BSD) variations such as FreeBSD, NetBSD,OpenBSD, and/or the like; Linux distributions such as Red Hat, Debian,Ubuntu, and/or the like); and/or the like operating systems.

An information server component 916 is a stored program component thatis executed by a CPU. The information server may be a conventionalInternet information server such as, but not limited to Apache SoftwareFoundation's Apache, Microsoft's Internet Information Server, and/or thelike. A user interface component 917 is a stored program component thatis executed by a CPU. The user interface component 917 may communicateto and/or with other components in a component collection, includingitself, and/or facilities of the like. Most frequently, the userinterface communicates with operating system component 915, otherprogram components, and/or the like. The user interface may contain,communicate, generate, obtain, and/or provide program component, system,user, and/or data communications, requests, and/or responses. Acryptographic server component 918 is a stored program component that isexecuted by a CPU 903, cryptographic processor 926, cryptographicprocessor interface 927, cryptographic processor device 926, and/or thelike. The cryptographic server component 918 facilitates the secureaccessing of resources on the IVTMC and facilitates the access ofsecured resources on remote systems; i.e., it may act as a client and/orserver of secured resources.

The database component 920 may be embodied in a database and its storeddata. The database is a stored program component, which is executed bythe CPU; the stored program component portion configuring the CPU toprocess the stored data. In one embodiment, the database component 920includes several tables 920 a-f. A thermal coefficient vector table(TCV) 920 a may include fields such as, but not limited to: tcv_id,tcv_type, tcv_value, tcv_date, and/or the like. A thermal properties(TP) table 920 b may include fields such as, but not limited to: tp_id,tp_value, hvac_id, zone_id, and/or the like. An weather estimations (WE)table 920 c may include fields such as, but not limited to: we_id,we_time, we_value, we_serviceProvider, and/or the like. A zone table 920d may include fields such as, but not limited to: zone_id,thermalDevice_id, hvac_id, tvc_id, and/or the like. A HVAC table 920 emay include fields such as, but not limited to: hvac_id, hvac_model,hvac_zoneID, hvac_avgPowerConsumption, hvac_avgEnergyEfficiency, and/orthe like. An estimations (EST) table 920f may include fields such as,but not limited to: est_id, est_time, est_type, est_value, est_zondeIDand/or the like. Any of the aforementioned tables may support and/ortrack multiple entities, accounts, users and/or the like.

The IVTMC component 919 may transform user weather estimations andthermal properties 920 b and/or the like, via various components (e.g.,comfort agent 120, comfort model 130, thermal model 140, thermal devices150 and weather model 160 of FIG. 1) as described herein, into estimatedtemperature, estimated energy consumption, estimated power consumptionand the like metrics. In one embodiment, the IVTMC component 919 takesinputs (e.g., weather estimations 920 c, thermal properties 920 b,and/or the like) etc., and transforms the inputs via various components(e.g., IVTMC component 919, and/or the like), into outputs (e.g.,estimated temperature, estimated energy consumption, estimated powerconsumption and/or the like).

In the preceding, reference is made to various embodiments. However, thescope of the disclosure is not limited to the specific describedembodiments. Instead, any combination of the described features andelements, whether related to different embodiments or not, iscontemplated to implement and practice contemplated embodiments.Furthermore, although embodiments can achieve advantages over otherpossible solutions or over the prior art, whether or not a particularadvantage is achieved by a given embodiment is not limiting of the scopeof the disclosure. Thus, the preceding aspects, features, embodimentsand advantages are merely illustrative and are not considered elementsor limitations of the appended claims except where explicitly recited ina claim(s).

The various embodiments disclosed herein can be implemented as a system,method or computer program product. Accordingly, aspects can take theform of an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that can allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects can take the form of a computer program productembodied in one or more computer-readable medium(s) havingcomputer-readable program code embodied thereon.

Any combination of one or more computer-readable medium(s) can beutilized. The computer-readable medium can be a non-transitorycomputer-readable medium. A non-transitory computer-readable medium canbe, for example, but not limited to, an electronic, magnetic, optical,electromagnetic, infrared, or semiconductor system, apparatus, ordevice, or any suitable combination of the foregoing. More specificexamples (a non-exhaustive list) of the non-transitory computer-readablemedium can include the following: an electrical connection having one ormore wires, a portable computer diskette, a hard disk, a random accessmemory (RAM), a read-only memory (ROM), an erasable programmableread-only memory (EPROM or Flash memory), an optical fiber, a portablecompact disc read-only memory (CD-ROM), an optical storage device, amagnetic storage device, or any suitable combination of the foregoing.Program code embodied on a computer-readable medium can be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thedisclosure can be written in any combination of one or more programminglanguages. Moreover, such computer program code can execute using asingle computer system or by multiple computer systems communicatingwith one another (e.g., using a local area network (LAN), wide areanetwork (WAN), the Internet, etc.). While various features in thepreceding are described with reference to flowchart illustrations and/orblock diagrams, a person of ordinary skill in the art will understandthat each block of the flowchart illustrations and/or block diagrams, aswell as combinations of blocks in the flowchart illustrations and/orblock diagrams, can be implemented by computer logic (e.g., computerprogram instructions, hardware logic, a combination of the two, etc.).Generally, computer program instructions can be provided to aprocessor(s) of a general-purpose computer, special-purpose computer, orother programmable data processing apparatus. Moreover, the execution ofsuch computer program instructions using the processor(s) produces amachine that can carry out a function(s) or act(s) specified in theflowchart and/or block diagram block or blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality and/or operation of possible embodiments ofvarious embodiments of the disclosure. In this regard, each block in theflowchart or block diagrams can represent a module, segment or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative embodiments, the functions noted in the blockcan occur out of the order noted in the figures. For example, two blocksshown in succession may, in fact, be executed substantiallyconcurrently, or the blocks can sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

It is to be understood that the above description is intended to beillustrative, and not restrictive. Many other embodiment examples areapparent upon reading and understanding the above description. Althoughthe disclosure describes specific examples, it is recognized that thesystems and methods of the disclosure are not limited to the examplesdescribed herein, but can be practiced with modifications within thescope of the appended claims. Accordingly, the specification anddrawings are to be regarded in an illustrative sense rather than arestrictive sense. The scope of the disclosure should, therefore, bedetermined with reference to the appended claims, along with the fullscope of equivalents to which such claims are entitled.

What is claimed is:
 1. A method, comprising: generating, by a controllerdevice, thermal coefficients at an adaptive filter bank to characterizesheat transfer of a volume associated with a thermal system; applying, bythe controller device, one or more filters to the thermal coefficientsbased on a sampling rate; responsive to the applying the filters,generating, by the controller device, one or more estimate thermalcoefficient thresholds based on the sampling rate; determining, by thecontroller device, whether at least one of the thermal coefficients thatis filtered satisfies at least one of the estimated thermal coefficientthresholds; and providing, by the controller device, alert informationindicative of a diagnostic event associated with the thermal systembased on the determining.
 2. The method of claim 1, wherein generatingthe thermal coefficients further comprises: identifying a thermal modelfor application with the thermal system; determining, based on thethermal model, an estimation error for a reference signal with respectto a primary signal associated with the volume; and adapting, based onthe adaptive filter, the thermal coefficients in view of the estimationerror to satisfy a solution associated with the volume.
 3. The method ofclaim 1, further comprising: adapting the sampling rate based on afilter operation associated with at least one of the filters.
 4. Themethod of claim 2, wherein the filter operation comprises at least oneinfinite impulse response filter.
 5. The method of claim 1, whereingenerating the estimate thermal coefficient thresholds furthercomprises: determining whether a sequence of thermal coefficient vectorssupport a definition of the diagnostic event.
 6. The method of claim 1,further comprising: determining whether the at least one thermalcoefficient exceeds an upper or lower boundary window associated withthe at least one estimated thermal coefficient threshold.
 7. The methodof claim 1, wherein the alert information indicates an anomalousoperation of a device associated with the volume.
 8. A system,comprising: a memory to store a plurality of thermal coefficient data;and a controller device, operatively coupled to the memory, to: generatethermal coefficients at an adaptive filter bank to characterizes heattransfer of a volume associated with a thermal system; apply or morefilters to the thermal coefficients based on a sampling rate; responsiveto applying the filters, generate one or more estimate thermalcoefficient thresholds based on the sampling rate; determine whether atleast one of the thermal coefficients that is filtered satisfies atleast one of the estimated thermal coefficient thresholds; and providealert information indicative of a diagnostic event associated with thethermal system based on the determining.
 9. The system of claim 8,wherein to generate the thermal coefficients, the controller device isfurther to: identify a thermal model for application with the thermalsystem; determine, based on the thermal model, an estimation error for areference signal with respect to a primary signal associated with thevolume; and adapt, based on the adaptive filter, the thermalcoefficients in view of the estimation error to satisfy a solutionassociated with the volume.
 10. The system of claim 8, wherein thecontroller device is further to: adapt the sampling rate based on afilter operation associated with at least one of the filters.
 11. Thesystem of claim 10, wherein the filter operation comprises at least oneinfinite impulse response filter.
 12. The system of claim 8, wherein togenerate the estimate thermal coefficient thresholds, the controllerdevice is further to: determine whether a sequence of thermalcoefficient vectors support a definition of the diagnostic event. 13.The system of claim 8, wherein the controller device is further to:determine whether the at least one thermal coefficient exceeds an upperor lower boundary window associated with the at least one estimatedthermal coefficient threshold.
 14. The system of claim 8, wherein thealert information indicates an anomalous operation of a deviceassociated with the volume.
 15. A non-transitory computer-readablestorage medium comprising executable instructions that when executed, bya controller device, cause the controller device to: apply, by thecontroller device, or more filters to the thermal coefficients based ona sampling rate; responsive to applying the filters, generate one ormore estimate thermal coefficient thresholds based on the sampling rate;determine whether at least one of the thermal coefficients that isfiltered satisfies at least one of the estimated thermal coefficientthresholds; and provide alert information indicative of a diagnosticevent associated with the thermal system based on the determining. 16.The non-transitory computer-readable storage medium of claim 15, whereinto generate the thermal coefficients, the controller device is furtherto: identify a thermal model for application with the thermal system;determine, based on the thermal model, an estimation error for areference signal with respect to a primary signal associated with thevolume; and adapt, based on the adaptive filter, the thermalcoefficients in view of the estimation error to satisfy a solutionassociated with the volume.
 17. The non-transitory computer-readablestorage medium of claim 15, wherein the controller device is further to:adapt the sampling rate based on a filter operation associated with atleast one of the filters.
 18. The non-transitory computer-readablestorage medium of claim 17, wherein the filter operation comprises atleast one infinite impulse response filter.
 19. The non-transitorycomputer-readable storage medium of claim 15, wherein to generate theestimate thermal coefficient thresholds, the controller device isfurther to: determine whether a sequence of thermal coefficient vectorssupport a definition of the diagnostic event.
 20. The non-transitorycomputer-readable storage medium of 15, wherein the controller device isfurther to: determine whether the at least one thermal coefficientexceeds an upper or lower boundary window associated with the at leastone estimated thermal coefficient threshold.